Question

Suppose x has a distribution with μ = 22 and σ = 17.

(a) If a random sample of size n = 40 is drawn, find μ_x, σ_x and P(22 ≤ x ≤ 24). (Round σ_x to two decimal places and the probability to four decimal places.)

μx =

σx =

P(22 ≤ x ≤ 24) =

(b) If a random sample of size n = 74 is drawn, find μ_x, σ_x and P(22 ≤ x ≤ 24). (Round σ_x to two decimal places and the probability to four decimal places.)

μx =

σx =

P(22 ≤ x ≤ 24) =

(c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).)
The standard deviation of part (b) is  ---Select--- the same as larger than smaller than part (a) because of the  ---Select--- smaller larger same sample size. Therefore, the distribution about μ_x is  ---Select--- wider narrower the same .

Answer 1

We have given,

Suppose x has a distribution with μ = 22 and σ = 17.

(a) If a random sample of size n = 40 is drawn,

Therefore,

=P[0<z<0.74]

=0.7704-0.5.....................................by using normal probability table.

=0.2704

(b) If a random sample of size n = 74 is drawn,

Therefore, P[22<x<24]

=P[0<z<1.01]

=0.8438-0.5.............................by using normal probability table.

=0.3438

(c)

The standard deviation of part (b) is smaller than part (a) because of the larger sample size. Therefore, the distribution about μx is the same .