DP Mathematics: Applications and Interpretation Questionbank

Find the probability that a bag selected at random weighs more than $1 \text{kg}$.

Find the standard deviation of the weights of these bags of apples.

Find the mean weight of a bag of apples.

Find the lower quartile of the weights of the sacks of potatoes.

The sacks of potatoes are transported in crates. There are $10$ sacks in each crate and the weights of the sacks of potatoes are independent of each other.

Find the probability that the total weight of the sacks of potatoes in a crate exceeds $500 \text{kg}$.

Find the probability that a sack is under its labelled weight.

A statistician in the company suggests it would be fairer if the company passes the inspection when the mean weight of five randomly chosen bags is greater than $950 \text{g}$.

Find the probability of passing the inspection if the statistician’s suggestion is followed.

In a coffee shop, the time it takes to serve a customer can be modelled by a normal distribution with a mean of 1.5 minutes and a standard deviation of 0.4 minutes.

Two customers enter the shop together. They are served one at a time.

Find the probability that the total time taken to serve both customers will be less than 4 minutes.

Clearly state any assumptions you have made.

Find

(i)     $\text{E}(X)$;

(ii)     $\text{Var}(X)$.

Explain why a normal distribution can be used to give an approximate model for $X$.

Use this model to find the values of $A$ and $B$ such that , where $A$ and $B$ are symmetrical about the mean of $X$.

Calculate the probability that he makes a Type II error.

State the distribution of $\overline{X}$ giving its mean and variance.

Find an unbiased estimate for $\mu$.

Find an unbiased estimate for ${\sigma }^2$.

Find a 90 % confidence interval for $\mu$.

Find the $p$-value for the test.

Write down the conclusion reached.

State the central limit theorem as applied to a random sample of size $n$, taken from a distribution with mean $\mu$ and variance ${\sigma }^2$.