The 240 members of a bowling club are listed alphabetically in the club's membership book. The committee wishes to select a sample of 30 members to fill in a questionnaire about the facilities the club offers.
Explain how the committee could use a table of random numbers to take a systematic sample.
Give one advantage of this method over taking a simple random sample.
The weights of pears, \(P\) grams, are normally distributed with a mean of 110 and a standard deviation of 8 . Geoff buys a bag of 16 pears.
Write down the distribution of \(\bar { P }\), the mean weight of the 16 pears.
Find \(\mathrm { P } ( 110 < \bar { P } < 113 )\).
The three tasks most frequently carried out in a garage are \(A , B\) and \(C\). For each of the tasks the times, in minutes, taken by the garage mechanics are assumed to be normally distributed with means and standard deviations given in the following table.
Task
Mean
Standard deviation
\(A\)
225
38
\(B\)
165
23
\(C\)
185
27
Assuming that the times for the three tasks are independent, calculate the probability that
the total time taken by a single randomly chosen mechanic to carry out all three tasks lies between 533 and 655 minutes,
a randomly chosen mechanic takes longer to carry out task \(B\) than task \(C\).