Question

The proportion of students who own a cell phone on college campuses across the country has increased tremendously over the past few years. It is estimated that approximately 95% of students now own a cell phone. Twenty five students are to be selected at random from a large university. Assume that the proportion of students who own a cell phone at this university is the same as nationwide. Let X = the number of students in the sample of 25 who own a cell phone.

What is the standard deviation of the number of students who own a cell phone in simple random samples of 25 students?

a. 1.0897
b. 0.0475
c. 1.1875
d. 1.35

Answer 1

Answer: option c is the correct answer.

Explanation:

It is estimated that approximately 95% of students now own a cell phone. This means that the probability of success, p of the event that a student owns a cellphone is

95/100 = 0.95

Therefore, the probability of failure, q of the event that a student owns a cellphone is expressed as

q = 1 - p

Therefore,

q = 1 - 0.95

q = 0.05

Standard deviation = √npq

Where

n represents the number of students sampled.

Therefore,

Standard deviation = √25 × 0.95 × 0.05 = 1.1875