Question

Suppose x has a distribution with μ = 11 and σ = 6.

(a) If a random sample of size n = 39 is drawn, find μx, σ x and P(11 ≤ x ≤ 13). (Round σx to two decimal places and the probability to four decimal places.)

μx =

σ x =

P(11 ≤ x ≤ 13) =

(b) If a random sample of size n = 70 is drawn, find μx, σ x and P(11 ≤ x ≤ 13). (Round σ x to two decimal places and the probability to four decimal places.)

μx =

σ x =

P(11 ≤ x ≤ 13)

Answer 1

Solution :

Given that,

mean = = 11

standard deviation = = 6

a)

n = 39

= 11

= / n = 6 / 39 = 0.96

P(11 13) = P((11 - 11) / 0.96 ( - ) / (13 - 11) / 0.96))

= P(0   Z 2.08)

= P(Z 2.08) - P(Z 0)

= 0.9812 - 0.5000

= 0.4812

Probability = 0.4812

b)

n = 70

= 11

= / n = 6 / 70 = 0.72

P(11   13) = P((11 - 11) / 0.72 ( - ) / (13 - 11) / 0.72))

= P(0   Z 2.78)

= P(Z 2.78) - P(Z 0)

= 0.9973 - 0.5000

= 0.4973

Probability = 0.4973