Question

a population has mean 48.4 and standard deviation 6.3 (a) find the mean and standard deviation of x for sample of size 64. (b) find the probability that the mean of a sample of size 64 will be less than 46.7

Answer 1

Solution :

Given that ,

mean = = 48.4

standard deviation = = 6.3

n = 64

a)

= = 48.4 and

= / n = 6.3/ 64 = 0.7875

b)

P( < 46.7) = P(( - ) / < (46.7 - 48.4) / 0.7875)

= P(z < -2.16)

= 0.0154 Using standard normal table,

Probability = 0.0154