Question

The proportion of adults who own a cell phone in a certain Canadian city is believed to be 65%. Forty adults are to be selected at random from the city. Let Xbe the number in the sample who own a cell phone. Under the assumptions given, the distribution of X is
A. Bin(40,0.65)
B. N(26,14)
C. Bin(40,26)
D. N(40,14)

Answer 1

Answer:

A. Bin(40,0.65)

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they have a cell phone, or they do not. The probability of an adult having a cell phone is independent of any other adult having a cell phone. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In function of its parameters, the distribution is written as: Bin(n,p).

The proportion of adults who own a cell phone in a certain Canadian city is believed to be 65%

This means that $p = 0.65$

Forty adults are to be selected at random from the city.

This means that $n = 40$.

Thus, we have Bin(40,0.65), and the correct answer is given by option A.