Question

a simple random sample of size 36 is taken from a normal population with mean 20 and standard deivation of 15. What is the probability the sample,mean,xbar based on these 36 observations will be within 4 units of the population mean. round to the hundreths place

Answer 1

Solution :

Given that,

mean = = 20

standard deviation = = 15

n = 36

=   = 20

= / n = 15 / 36 = 2.5

P(16 < < 24)  

= P[(16 - 20) / 2.5 < ( - ) / < (24 - 20) / 2.5)]

= P(-1.60 < Z < 1.60 )

= P(Z < 1.60) - P(Z < -1.60)

Using z table,  

= 0.95 - 0.05

= 0.90