Question

A random variable is normally distributed. It has a mean of 245 and a standard deviation of 21.

e.) For a sample of size 35, state the mean of the sample mean and the standard deviation of the sample mean.

f.) For a sample of size 35, find the probability that the sample mean is more than 241.

g.) Compare your answers in part c and f. Why is one smaller than the other?

Answer 1

Solution :

Given that ,

mean = = 245

standard deviation = = 21

(e)

n = 35

= 245 and

= / n = 21 / 35 = 3.5496

(f)

P( > 241) = 1 - P( < 241)

= 1 - P(( - ) / < (241 - 245) / 3.5496)

= 1 - P(z < -1.13)

= 1 - 0.1292

= 0.8708

P( > 241) = 0.8708

Probability = 0.8708

(g)

c part is not present here .