The proportion of students who own a cell phone on college campuses across the c

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 90% of students now own a cell phone. Fifteen 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 15 who own a cell phone. What is the appropriate distribution of X? Select one: a. X is Bin(15, 13.5) b. X is Bin(15, 0.9) c. X is N(15, 0.9) d. X is N(13.5, 1.16) 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 90% of students now own a cell phone. Fifteen 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 15 who own a cell phone. On average, how many students will own a cell phone in simple random sample of 15 students? Select one: A. 13 b. 14 c. 13.5 d. 9

Explanation / Answer

Let there be n independent bernoulli trials.(i.e trials where the outcome is a yes/no. eg here there are 15 independent bernoulli trials where in each trial, each of the 15 students are asked if they have a mobile phone or not. the answer will be binary type. i.e either they have a cell phone or they do not have it)

Let the probability of success i.e getting Yes for an answer in each of these n(here n=15) trials be p ( here p is given to be 90%, i.e 0.9).

Then the number of success, i.e here the total number of students out of the 15 students who have a cell phone i.e X is said to follow a Bin(n,p) (here Bin(15,0.9) distn).

So X follows Bin(15,0.9) distn.

Answer is (b)

The second question wants the expected number of stuents having a cell phone , i.e the Expectation of X where X follows Bin(15,0.9) distn.

E(X) = np

So here E(X) = 15*0.9 = 13.5 (answer is c.)

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