Respuesta :
Complete Question
The complete question is shown on the uploaded image Â
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  [tex]p = 0.90[/tex]
  The  sample  size is  n =  15
Generally the appropriate distribution for X is mathematically  represented as
   [tex]X \ is \ B( n , p )[/tex]
So Â
    [tex]X \ is \ B( 15 , 0.90 )[/tex]
Generally the number students that  own a cell phone in a simple random sample of 15 students is mathematically represented as
       [tex]\mu = n * p[/tex]
       [tex]\mu = 15 * 0.90[/tex]
       [tex]\mu = 13.5[/tex]
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
        [tex]\sigma = \sqrt{ n * p * q }[/tex]
Where  q is mathematically evaluated as
     [tex]q = 1- p[/tex]
      [tex]q = 1- 0.90[/tex]
      [tex]q = 0.10[/tex]
      [tex]\sigma = \sqrt{ 15 * 0.90 * 0.10 }[/tex]
      [tex]\sigma = 1.16[/tex]
Generally the probability that all students in a simple random sample of 15 students own a cell phone is mathematically represented as
  [tex]P(X = 15) = \left 15} \atop {}} \right.C_{15} * p^{15} * q^{15 - 15}[/tex]  Â
   [tex]P(X = 15) = \left 15} \atop {}} \right.C_{15} * (0.90)^{15} * (0.10 )^{15 - 15}[/tex]
From the combination calculator  is    [tex]\left 15} \atop {}} \right.C_{15} = 1[/tex]
   [tex]P(X = 15) = 1 * 0.205891 * 1[/tex]
   [tex]P(X = 15) = 0.206[/tex]
The appropriate distribution for X is M(15, 0.9).
On average 1.345 students will own a cell phone in a simple random sample of 15 students.
The standard deviation of the number of students who own a cell phone in a simple random sample of 15 students is 1.16.
The probability that all students in a simple random sample of 15 students own a cell phone is 0.206.
Given that,
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.
According to the question,
Let X = the number of students in the sample of 15 who own a cell phone.
1. The appropriate distribution for X is,
the sample size is n equals 15 and the proportion of the cell phone is 90% = 0.9.
The appropriate distribution for X is M(15, 0.9).
2. On average students will own a cell phone in a simple random sample of 15 students is,
[tex]\mu = n \times p\\\\\mu = 15 \times 0.9\\\\\mu = 1.345[/tex]
On average 1.345 students will own a cell phone in a simple random sample of 15 students.
3. The standard deviation of the number of students who own a cell phone in a simple random sample of 15 students is,
[tex]\rm \sigma = \sqrt{n \times p \times q}\\\\\sigma = \sqrt{n \times p \times (1-q)}\\\\\sigma = \sqrt{15 \times 0.9 \times (1-0.9)}\\\\\sigma = \sqrt{15 \times 0.9 \times 0.1}\\\\\sigma = 1.16[/tex]
The standard deviation of the number of students who own a cell phone in a simple random sample of 15 students is 1.16.
4. The probability that all students in a simple random sample of 15 students own a cell phone is,
[tex]\rm P(X=15) = 15_C_{15} \times p^{15} \times q^{15-15}\\\\P(X=15) = 1 \times (0.90)^{15 }\times (0.10)^0\\\\P(X=15) = 1 \times 0.206\times 1\\\\P(X=15) = 0.206[/tex]
The probability that all students in a simple random sample of 15 students own a cell phone is 0.206.
For more details refer to the link given below.
https://brainly.com/question/17521208
