Question

A population has a mean of 128 and a standard deviation of 32. Suppose a sample of size 64 is selected and

x

is used to estimate μ. (Round your answers to four decimal places.)

(a)

What is the probability that the sample mean will be within ±5 of the population mean?

Answer 1

Solution :

Given that ,

mean = = 128

standard deviation = = 32

n = 64

=   = 128

= / n = 32 / 64 = 4

128 ± 5 = 123, 133

P(123 < < 133)

= P[(123 - 128) /4 < ( - ) / < (133 - 128) / 4)]

= P( -1.25 < Z < 1.25 )

= P(Z < 1.25 ) - P(Z < -1.25 )

Using z table,  

= 0.8944 - 0.1056

= 0.7888