DP Mathematics: Analysis and Approaches Questionbank

Find the probability that a randomly selected packet has a weight less than $100 \text{g}$.

The probability that a randomly selected packet has a weight greater than $w$ grams is $0.444$. Find the value of $w$.

A packet is randomly selected. Given that the packet has a weight greater than $105 \text{g}$, find the probability that it has a weight greater than $110 \text{g}$.

From a random sample of $500$ packets, determine the number of packets that would be expected to have a weight lying within $1.5$ standard deviations of the mean.

Packets are delivered to supermarkets in batches of $80$. Determine the probability that at least $20$ packets from a randomly selected batch have a weight less than $95 \text{g}$.

Sketch a diagram to represent this information.

Show that $m=15.7$.

Find the probability that Emlyn plays between $13 \text{minutes}$ and $18 \text{minutes}$ in a game.

Find the probability that Emlyn plays more than $20 \text{minutes}$ in a game.

Find the value of $x$.

Find the probability he plays between $13 \text{minutes}$ and $18 \text{minutes}$ in one game and more than $20 \text{minutes}$ in the other game.

Find the expected number of successful shots Emlyn will make on Monday, based on the results from Saturday and Sunday.

Emlyn claims the results from Saturday and Sunday show that his expected number of successful shots will be more than Johan’s.

Determine if Emlyn’s claim is correct. Justify your reasoning.

By stating and solving an appropriate equation, show, correct to two decimal places, that $\mu =32.29$.

Find the $86$th percentile time to complete the jigsaw puzzle.

Find the probability that a randomly chosen person will take more than $30$ minutes to complete the jigsaw puzzle.

Given that a bag is not rejected, find the probability that it has a mass greater than $1005$ grams.

Find the probability that a bag selected at random is rejected.

Estimate the number of bags which will be rejected from a random sample of $100$ bags.

Given that $2\%$ of the flight times are longer than $82$ minutes, find the value of $\sigma$.

Find the probability that a randomly selected flight will have a flight time of more than $80$ minutes.

Given that a flight between the two cities takes longer than $80$ minutes, find the probability that it takes less than $82$ minutes.

Find the probability that more than $6$ of the flights on this particular day will have a flight time of more than $80$ minutes.

Find the expected number of flights that will have a flight time of more than $80$ minutes.

Find the probability that a randomly selected chocolate muffin weighs less than $61 \text{g}$.

Find the probability that the randomly selected muffin weighs less than $61 \text{g}$.

Rachel and Sophia are competing in a javelin-throwing competition.

The distances, $R$ metres, thrown by Rachel can be modelled by a normal distribution with mean $56.5$ and standard deviation $3$.

The distances, $S$ metres, thrown by Sophia can be modelled by a normal distribution with mean $57.5$ and standard deviation $1.8$.

In the first round of competition, each competitor must have five throws. To qualify for the next round of competition, a competitor must record at least one throw of $60$ metres or greater in the first round.

Find the probability that only one of Rachel or Sophia qualifies for the next round of competition.

On a randomly selected day, find the probability that Suzi’s drive to work will take longer than $45$ minutes.

Find E(Y).

Hence, find the probability that a seashell selected at random has a length greater than 26 mm.

Find $\sigma$, the standard deviation of X.

Find P(24.15 < X < 25).

A seashell selected at random has a length less than 26 mm.

Find the probability that its length is between 24.15 mm and 25 mm.

Find the probability that exactly three of these seashells have a length greater than 26 mm.

Given that $\mu =253$ and $\sigma =1.5$ find the probability that a randomly chosen packet of biscuits is underweight.

Calculate the new value of $\mu$ giving your answer correct to two decimal places.

Calculate the new value of $\sigma$.

Find the probability that a wolf selected at random is at least 5 years old.

Eight wolves are independently selected at random and their ages recorded.

Find the probability that more than six of these wolves are at least 5 years old.

Sketch the probability density function for X, and shade the region representing P(μ − 2σ < X < μ + σ).

Find the value of P(μ − 2σ < X < μ + σ).

Find the value of k for which P(μ − kσ < X < μ + kσ) = 0.5.

Find the probability that a runner selected at random will complete the marathon in less than 3 hours.

Calculate $T_1$.

Find the standard deviation of the times taken by female runners.

Calculate the probability that, on a randomly selected day, Timmy makes a profit.

The shop is open for 24 days every month.

Calculate the probability that, in a randomly selected month, Timmy makes a profit on between 5 and 10 days (inclusive).

Find the value of $\mu$ and the value of $\sigma$.

Find the probability that a randomly selected Infiglow battery will have a life of at least 15 hours.

$\text{P}\left(X>\mu +5\right)$.

.

Find $\mu$ and $\sigma$.

Find .

It is given that one in five cups of coffee contain more than 120 mg of caffeine.
It is also known that three in five cups contain more than 110 mg of caffeine.

Assume that the caffeine content of coffee is modelled by a normal distribution.
Find the mean and standard deviation of the caffeine content of coffee.

Write down $\text{P}(X>107)$.

Find .

Find .

Find the probability that an orange weighs between 289 g and 310 g.

Find the standardized value for 289 g.

Hence, find the value of σ.

To the nearest gram, find the minimum weight of an orange that the grocer will buy.

Find the probability that the grocer buys more than half the oranges in a box selected at random.

The grocer selects two boxes at random.

Find the probability that the grocer buys more than half the oranges in each box.

Write down the value of k.

Show that μ = 106.

Find P(M < 95) .

Find the probability that a bag of apples selected at random contains at most one small apple.

Find the expected number of bags in this crate that contain at most one small apple.

Find the probability that at least 48 bags in this crate contain at most one small apple.

Find .

Find the value of $\mu$.

Find $\lambda$.

Given that $Y>9$, find .

The heights of adult males in a country are normally distributed with a mean of 180 cm and a standard deviation of $\sigma \text{ cm}$. 17% of these men are shorter than 168 cm. 80% of them have heights between $(192-h)\text{ cm}$ and 192 cm.

Find the value of $h$.

Find P(−1.6 < $z$ < 2.4). Write your answer in terms of $a$ and $b$.

Given that $z$ > −1.6, find the probability that z < 2.4 . Write your answer in terms of $a$ and $b$.

Write down the standardized value for $x=1$.

It is also known that P($x$ > 2) = $b$.

Find $s$.

Show that event A and event D are not independent.

Find $\text{P}\left(A\cap D^{\prime }\right)$.

 Given that all passengers for a flight arrive on time, find the probability that the flight does not depart on time.

Find the value of $\sigma$.

All flights have two pilots. Find the percentage of flights where both pilots flew more than 30 hours last week.

A person is selected at random from Group X. Find the probability that their reaction time is greater than 0.65 seconds.

The probability that the reaction time of a person in Group Y is greater than 0.65 seconds is 0.396. Find the value of σ.

A randomly selected participant has a reaction time greater than 0.65 seconds. Find the probability that the participant is in Group X.

Ten of the participants with reaction times greater than 0.65 are selected at random. Find the probability that at least two of them are in Group X.

Given that 5.3% of newborn babies have a low birth weight, find $w$.

Find the probability that a student, chosen at random arrives at least 60 minutes after the school opens.

Find the probability that a student, chosen at random arrives between 45 minutes and 55 minutes after the school opens.

A second school, Mulberry Park, also opens at 08:00 every morning. The arrival times of the students at this school follows exactly the same distribution as Malthouse school.

Given that, on one morning, 15 students arrive at least 60 minutes after the school opens, estimate the number of students at Mulberry Park school.

Find the probability that this applicant took at least 40 minutes to complete the test.

Find the value of $k$.

Estimate the number of applicants who completed the test in less than 25 minutes.

Write down the probability that the mass of one of these corncobs is greater than 400 grams.

Find the value of $a$.

Estimate the interquartile range of the distribution.

Calculate the mean test grade of the students;

Calculate the standard deviation.

Find the median test grade of the students.

Find the interquartile range.

Find the probability that this student scored a grade 5 or higher.

Given that the first student chosen at random scored a grade 5 or higher, find the probability that both students scored a grade 6.

Calculate the probability that a student chosen at random spent at least 90 minutes preparing for the test.

Calculate the expected number of students that spent at least 90 minutes preparing for the test.

Draw a diagram that shows this information.

(i)     Find the probability that a box of cereal, chosen at random, is sold.

(ii)     Calculate the manufacturer’s expected daily income from these sales.

Calculate the manufacturer’s expected daily recycling cost.

Calculate the value of $w$.

Find the probability that a basketball player has a weight that is less than 61 kg.

In a training session there are 40 basketball players.

Find the expected number of players with a weight less than 61 kg in this training session.

Sketch a normal curve to represent this probability.

Find the value of q.

Given that P(W > k) = 0.225 , find the value of k.

For this test state the null hypothesis.

For this test find the p-value.

State a conclusion for this test. Justify your answer.

Find the price that is two standard deviations above the mean price.

Find the probability that the price of a kilogram of tomatoes, chosen at random, will be between 2.00 and 3.00 euro.

To stimulate reasonable pricing, the city offers a free permit to the sellers whose price of a kilogram of tomatoes is in the lowest 20 %.

Find the highest price that a seller can charge and still receive a free permit.

In the following table, write down the letter of the corresponding graph next to the given mean and standard deviation.

Find the probability that a suitcase weighs less than 15 kg.

Any suitcase that weighs more than $k$ kg is identified as excess baggage.
19.6 % of the suitcases at this airport are identified as excess baggage.

Find the value of $k$.

Runners in an athletics club have season’s best times for the 100 m, which can be modelled by a normal distribution with mean 11.6 seconds and standard deviation 0.8 seconds. To qualify for a particular competition a runner must have a season’s best time of under 11 seconds. A runner from this club who has qualified for the competition is selected at random. Find the probability that he has a season’s best time of under 10.7 seconds.

Find $b$ so that .

It is given that $\text{P}\left(X>20\right)=0.112$.

Find .

Calculate the probability a flight is not late.

Find the value of $m$.

Calculate the probability that at least $7$ of these flights are on time.

Given that at least $7$ of these flights are on time, find the probability that exactly $10$ flights are on time.

SpeedWay increases the number of flights from city $\text{A}$ to city $\text{B}$ to $20$ flights each week, and improves their efficiency so that more flights are on time. The probability that at least $19$ flights are on time is $0.788$.

A flight is chosen at random. Calculate the probability that it is on time.