Question

The heights of a certain population of corn plants follow a distribution with mean 145 cm and standard deviation 22 cm.

(a) Suppose we were to choose a sample of size 16 at random from the population, what would be the mean and standard deviation of the sample average?

(b) Suppose we were to choose a sample of size 16 at random from the population, what would be the distribution of the sample average?

(c) Suppose we were to choose a sample of size 36 at random from the population, what would be the mean and standard deviation of the sample average?

(d) Suppose we were to choose a sample of size 36 at random from the population, what would be the distribution of the sample average?

(e) Answer part (a) and part (b), if you know the height of the population of corn plants follow a normal distribution.

Answer 1

Answer:

Given,

Mean = 145

Standard deviation = 22

a)

To determine the mean and standard deviation of the sample average

Here n = 15

Mean = $\mu _{\bar{x}}$ = $\mu _$ = 145

Standard deviation = $\sigma _{\bar{x}}$ = $\sigma$/sqrt(n)

substitute values

= 22/sqrt(16)

= 22/4

Standard deviation = 5.5

b)

Here the distribution of the sample average is approximately normal

c)

To determine the mean and standard deviation of the sample average

Here n = 36

Mean = $\mu _{\bar{x}}$ = $\mu _$ = 145

Standard deviation = $\sigma _{\bar{x}}$ = $\sigma$/sqrt(n)

substitute values

= 22/sqrt(36)

= 22/6

= 3.6666

Standard deviation = 3.67

d)

Here the distribution of the sample average is approximately normal.