Question

A normally distributed population has a mean of 425 and a standard deviation of 48

a. Determine the probability that a random sample of size

16

selected from this population will have a sample mean less than

400

b. Determine the probability that a random sample of size

9

selected from the population will have a sample mean greater than or equal to

469

Answer 1

Solution :

Given that,

mean = = 425

standard deviation = = 48

a) n = 16

= = 425

= / n = 48 / 16 = 12

P( < 400) = P(( - ) / < (400 - 425) / 12)

= P(z < -2.08)

Using z table

= 0.0188

b) n = 9

= = 425

= / n = 48 / 9 = 16

P( 469) = 1 - P( 469)

= 1 - P[( - ) / (469 - 425) / 16 ]

= 1 - P(z 2.75)   

= 1 - 0.9970

= 0.0030