Question

A random sample of n = 25 is selected from a normal population with mean

μ = 101

and standard deviation

σ = 13.

(a) Find the probability that x exceeds 107. (Round your answer to four decimal places.)

(b) Find the probability that the sample mean deviates from the population mean μ = 101 by no more than 2. (Round your answer to four decimal places.)

Answer 1

Solution :

Given that ,

mean = = 101

standard deviation = = 13

n = 25

= and

= / n = 13 / 25= 2.6

a)

P( > 107) = 1 - P( < 107)

= 1 - P(( - ) / < (107 - 101) / 2.6)

= 1 - P(z < 2.31)

= 1 - 0.9896 Using standard normal table.

= 0.0104

Probability = 0.0104

b)

P(99 < < 103) = P((99 - 101) /2.6 <( - ) / < (103 - 101) / 2.6))

= P(-0.77 < Z < 0.77)

= P(Z < 0.77) - P(Z < -0.77) Using standard normal table,  

= 0.7794 - 0.2206

= 0.5587

Probability = 0.5587