Question

A population of values has a distribution with 37.9 and standard deviation of 94.1 . You intend to draw a random sample of size 79. According to the Central Limit Theorem: (a) What is the mean of the distribution of sample means? (

b) What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.)

c) In a random sample of n=79, what is the probability that its random sample mean is more than 37.6? Round to three decimal places.

(d) In a random sample of n=79, what is the probability that its random sample mean is less than 21? Give your answer to three decimal places.

Answer 1

Solution :

Given that ,

mean = = 37.9

standard deviation = = 94.1

n = 79

a) = = 37.9

b) = / n = 94.1 / 79 = 10.59

c) P( > 37.6) = 1 - P( < 37.6)

= 1 - P[( - ) / < (37.6 - 37.9) / 10.59 ]

= 1 - P(z < -0.03)

Using z table,    

= 1 - 0.488

= 0.512

d) P( < 21) = P(( - ) / < (21 - 37.9) / 10.59)

= P(z < -1.60)

Using z table

= 0.055