Question

According to a report from a business intelligence​ company, smartphone owners are using an average of 23 apps per month. Assume that number of apps used per month by smartphone owners is normally distributed and that the standard deviation is 4. Complete parts​ (a) through​ (d) below.

A) If you select a random sample of 36 smartphone​ owners, what is the probability that the sample mean is between 22.5and 23.5?

B) If you select a random sample of 36 smartphone​ owners, what is the probability that the sample mean is between 22 and 23

C) If you select a random sample of 100 smartphone​ owners, what is the probability that the sample mean is between 22.5 and 23.5​?

Answer 1

Solution :

A)

= / n = 4 / 36 = 0.6667

= P[(22.5 - 23) / 0.6667 < ( - ) / < (23.5 - 23) / 0.6667)]

= P(-0.75 < Z < 0.75)

= P(Z < 0.75) - P(Z < -0.75)

= 0.7734 - 0.2266

= 0.5468

Probability = 0.5468

B)

= P[(22 - 23) / 0.6667 < ( - ) / < (23 - 23) / 0.6667)]

= P(-1.50 < Z < 0)

= P(Z < 0) - P(Z < -1.50)

= 0.5 - 0.0668

= 0.4332

Probability = 0.4332

C)

= / n = 4 / 100 = 0.4

= P[(22.5 - 23) / 0.4 < ( - ) / < (23.5 - 23) / 0.4)]

= P(-1.25 < Z < 1.25)

= P(Z < 1.25) - P(Z < -1.25)

= 0.8944 - 0.1056

= 0.7888

Probability = 0.7888