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.
1. What is the appropriate distribution forX? **N = Normal, B = Binomial?
A. X is M(15, 0.9).
B, X is B(15, 09).
C. Xis B(15, 13.5).
D. Xis N(13,5, 1.16).
2. On average, how many students will own a cell phone in a simple random sample of 15 students?
a. 9.
b. 13
c. 13.5.
d. 14 17.
3. What is the standard deviation of the number of students who own a cell phone in a simple random sample of 15 students?
a. 0.077.
b. 0.09.
c. 1.16.
d. 1.35.
4. What is the probability that all students in a simple random sample of 15 students own a cell phone?
a. 0.
b. 0.1.
c. 0.206.
d. 0.9.

Answer 1

Complete Question

The complete question is shown on the uploaded image  

Answer:

1 ) The correct option B

2) The correct option is  C

3)  The correct option is  C

4)  The correct option is  C

Step-by-step explanation:

From the question we are told that

   The proportion that own a cell phone  is  $p = 0.90$

    The  sample  size is  n =  15

Generally the appropriate distribution for X is mathematically  represented as

      $X \ is \ B( n , p )$

So  

       $X \ is \ B( 15 , 0.90 )$

Generally the number students that  own a cell phone in a simple random sample of 15 students is mathematically represented as

              $\mu = n * p$

              $\mu = 15 * 0.90$

              $\mu = 13.5$

Generally the standard deviation of the number of students who own a cell phone in a simple random sample of 15 students is mathematically represented as

                $\sigma = \sqrt{ n * p * q }$

Where  q is mathematically evaluated as

          $q = 1- p$

           $q = 1- 0.90$

           $q = 0.10$

            $\sigma = \sqrt{ 15 * 0.90 * 0.10 }$

            $\sigma = 1.16$

Generally the probability that all students in a simple random sample of 15 students own a cell phone is mathematically represented as

   $P(X = 15) = \left 15} \atop {}} \right.C_{15} * p^{15} * q^{15 - 15}$    

     $P(X = 15) = \left 15} \atop {}} \right.C_{15} * (0.90)^{15} * (0.10 )^{15 - 15}$

From the combination calculator  is      $\left 15} \atop {}} \right.C_{15} = 1$

     $P(X = 15) = 1 * 0.205891 * 1$

      $P(X = 15) = 0.206$