Question

Question 12

1. A student takes an 8-question, true-false exam and guesses on each question. Find the probability of passing if the lowest passing grade is 6 correct out of 8.

   	a.	0.109
   	b.	0.227
   	c.	0.144
   	d.	0.164

  

Question 13

1. R.H. Bruskin Associates Market Research found that 30% of Americans do not think having a college education is important to succeed in the business world. If a random sample of 5 Americans is selected, find this probability: At most three people will agree with that statement.

   	a.	0.811
   	b.	0.837
   	c.	0.499
   	d.	0.969

  

Question 14

1. R.H. Bruskin Associates Market Research found that 30% of Americans do not think having a college education is important to succeed in the business world. If a random sample of 5 Americans is selected, find this probability: At least two people will agree with that statement.

   	a.	0.471
   	b.	0.936
   	c.	0.829
   	d.	0.811

  

Question 15

1. In a restaurant, a study found that 25% of all patrons smoked. If the seating capacity of the restaurant is 80 people, find the variance of the number of smokers.

   	a.	3.87
   	b.	19.8
   	c.	15
   	d.	4.45

Answer 1

a)

A student takes an 8-question, true-false exam and guesses on each question.

Thus he have 2 choises , Probability of selecting TRUE is 0.5 and Probability of selecting FALSE is 0.5

Now we need to find probability of passing if the lowest passing grade is 6 correct out of 8.

Now Let p be probability of sucess .

Here let p be probability of selecting option TRUE

Thus p=0.5

We have 8 question , thus n = 8

It follows binomial process with n =8 and p =0.5

We need to find getting 6 correct out of 8. i.e x=6

X ~ B( n=6 , p=0.5 )

P(X=x) =

Thus required probability will be given by

P( X=6 ) =    = 28 * 0.56 * 0.52             { p=0.5 and = 28

P( X=6 ) = 0.109375

Hence required Probability is 0.109375

Thus , probability of passing if the lowest passing grade is 6 correct out of 8 0.109

Correct option a) 0.109

b)

let p be probability of succes

30% of Americans do not think having a college education is important to succeed in the business world .

Then p =0.30

Random sample of 5 Americans is selected, hence n=5

We need to find this probability: At most three people will agree with that statement.

Thus we need to find probabilty than 3 or less than 3 people will agree with that statement.

Here X ~ B( n =5 , p=0.3)

P(X=x) =

Thus required probability will be given by

P( X 3 ) = P( X = 0 ) + P( X = 1 ) + P( X = 2 ) + P( X = 3 )

             =    + + +   

                 = 0.16807 + 0.36015 + 0.3087 + 0.1323

P( X 3 ) = 0.96922

Hence required Probability is 0.96922

Thus Probability that At most three people will agree with that statement is 0.96922

Correct option d) 0.969

c)

This time p =0.3 , n =5

We need to find probability: At least two people will agree with that statement.

Thus this time we need to find probabilty than 2 or more than 2 people will agree with that statement.

Here X ~ B( n =5 , p=0.3)

P(X=x) =

We need to find

P( X 2) = 1 - P( X < 2 )

Now , 1 - P( X < 2 ) = 1 - P( X = 0 ) - P( X = 1 )

                                    = 1 -    -

                                    = 1 - 0.16807 - 0.36015

            1 - P( X < 2 ) = 0.47178

Hence , P( X 2) = 1 - P( X < 2 ) = 0.47178

P( X 2) = 0.47178

Hence required Probability is 0.47178

Thus Probability that At least two people will agree with that statement. is 0.47178

Correct option a) 0.471

d)

In a restaurant, a study found that 25% of all patrons smoked.

let p be probability of smokers , thus p=0.25

Seating capacity of the restaurant is 80 people , thus n=80

Need to find the variance of the number of smokers

For these case X ~ B( n =80 , p =0.25 )

Variance is gven by

Var(X) = n * p * ( 1-p )

Var(X) = 80 * 0.25 * 0.75 = 15

Var(X) = 15

Hence , the variance of the number of smokers is 15

Correct option is c) 15