Question

Suppose a simple random sample of size nequals36 is obtained from a population with mu equals 82 and sigma equals 18. ​(a) Describe the sampling distribution of x overbar. ​(b) What is Upper P left parenthesis x overbar greater than 88 right parenthesis​? ​(c) What is Upper P left parenthesis x overbar less than or equals 76 right parenthesis​? ​(d) What is Upper P left parenthesis 78.1 less than x overbar less than 87.55 right parenthesis​?

Answer 1

Solution :

Given that ,

mean = = 82

standard deviation = = 18

n = 36

(a)

= 82 and

= / n = 18 / 36 = 18 / 6 = 3

(b)

P( > 88) = 1 - P( < 88)

= 1 - P(( - ) / < (88 - 82) / 3)

= 1 - P(z < 1.33)

= 1 - 0.9082

= 0.0918

Probability = 0.0918

(c)

P( < 76) = P(( - ) / < (76 - 82) / 3)

= P(z < -2)

= 0.0228

Probability = 0.0228

(d)

P(78.1 < < 87.55) = P((78.1 - 82) / 3 <( - ) / < (87.55 - 82) / 3))

= P(-1.3 < Z < 1.85)

= P(Z < 1.85) - P(Z < -1.3)

= 0.9678 - 0.0968

= 0.871

Probability = 0.871