In: Statistics and Probability
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
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