Question

A manufacturer produces widgets whose lengths are normally distributed with a mean of 17.3 cm and standard deviation of 2 cm.

A. If a widget is selected at random, what is the probability it is greater than 17.4 cm.? Round to dour decimal places

B. What is the standard deviation of the average of samples of size 32 ? Round answer to four decimal places

C. What is the probability the average of a sample of size 32 is greater than 17.4 cm? Round answer to four decimal places.

Answer 1

A)

Let X denote the length of the widget (in cm). Then

Required probability =

B)

Using Central Limit theorem, we know,

So,

C)

Now,

Required probability =