DP Mathematics: Analysis and Approaches Questionbank

Find the probability that it will take Fiona between $15$ minutes and $30$ minutes to walk to the bus stop.

Find $\sigma$.

Find the probability that the bus journey takes less than $45$ minutes.

Find the probability that Fiona will arrive on time.

This year, Fiona will go to school on $183$ days.

Calculate the number of days Fiona is expected to arrive on time.

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 $2\%$ 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 $\text{P}\left(\mu -1.5\sigma <X<\mu +1.5\sigma \right)$.

medium.

large.

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

The selling prices of the different categories of avocado at this supermarket are shown in the following table:

The supermarket pays the farm $\$ 200$ for the avocados and assumes it will then sell them in exactly the same proportion as purchased from the farm.

According to this model, find the minimum number of avocados that must be sold so that the net profit for the supermarket is at least $\$ 438$.

premium.

Find the value of $\sigma$.

Find the value of $\sigma$.

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.