Mathematics, 18.02.2020 22:57 onewaydemon

Nationwide survey of college seniors by the University of Michigan revealed that almost 70% disapprove of daily pot smoking, according to a report in Parade. If 12 seniors are selected at random and asked their opinion, find the probability that the number who disapprove of smoking pot daily is

anywhere from 7 to 9;

at most 5;

not less than 8.

Answers: 2

Show answers

Answers

Answer from: SJ9320

The probability of number who disapprove of smoking pot daily is from 7 to 9 is 0.6293.

The probability of number who disapprove of smoking pot daily is at most 5 is 0.038601

The probability of number who disapprove of smoking pot daily is is not less than 8 is 0.723655.

Step-by-step explanation:

The number of seniors that disapprove smoking pot daily X follows binomial distribution with n=12 and p=0.7 because

1. The opinion of seniors are independent.

2. There are two possible outcome approve or disapprove.

3. The probability of seniors disapproves smoking pot daily is constant for each trail i.e. p=0.7.

4. The opinion is asked from 12 senior i.e. fixed number of trails.

The probability of the number of seniors that disapprove smoking pot daily can be computed as

$P(X=x)=nCxp^{x} q^{n-x}$

Here, n=12, p=0.7 and q=0.3.

P(number who disapprove of smoking pot daily is from 7 to 9)=P(7≤X≤9)=?

P(7≤X≤9)=P(X=7)+P(X=8)+P(X=9)

$P(X=7)=12C7(0.7)^{7} 0.3^{5}$ = 0.158496

$P(X=8)=12C8(0.7)^{8} 0.3^{4}$ = 0.231140

$P(X=9)=12C9(0.7)^{9} 0.3^{3}$ = 0.239700

P(7≤X≤9)=0.158496+0.231140+0.239700

P(7≤X≤9)=0.6293

The probability of number who disapprove of smoking pot daily is from 7 to 9 is 0.6293.

P(number who disapprove of smoking pot daily is at most 5)=P(X≤5)=?

P(X≤5)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)

$P(X=0)=12C0(0.7)^{0} 0.3^{12}$ = 0.000001

$P(X=1)=12C1(0.7)^{1} 0.3^{11}$ = 0.000015

$P(X=2)=12C2(0.7)^{2} 0.3^{10}$ = 0.000191

$P(X=3)=12C3(0.7)^{3} 0.3^{9}$ = 0.001485

$P(X=4)=12C4(0.7)^{4} 0.3^{8}$ = 0.007798

$P(X=5)=12C5(0.7)^{5} 0.3^{7}$ = 0.029111

P(X≤5)=0.000001+ 0.000015+ 0.000191+ 0.001485+ 0.007798+ 0.029111

P(X≤5)=0.038601

The probability of number who disapprove of smoking pot daily is at most 5 is 0.038601.

P(number who disapprove of smoking pot daily is not less than 8)=P(X≥8)=?

P(X≥8)=1- P(X<8)

P(X≥8)= 1-P(X≤7)

P(X≤7)=P(X≤5)+P(X=6)+P(X=7)

$P(X=6)=12C6(0.7)^{6} 0.3^{6}$ = 0.079248

$P(X=7)=12C7(0.7)^{7} 0.3^{5}$ = 0.158496

P(X≤7)=0.038601+ 0.079248+ 0.158496

P(X≤7)=0.276345

P(X≥8)=1-0.276345

P(X≥8)=0.723655

The probability of number who disapprove of smoking pot daily is is not less than 8 is 0.723655.

Answer from: Quest

the bottom of the spinner is not flat.

step-by-step explanation:

Answer from: Quest

6hope this ! ! ’

Another question on Mathematics

Mathematics, 21.06.2019 20:50

Find the equation of a line that is perpendicular to line g that contains (p, q). coordinate plane with line g that passes through the points negative 3 comma 6 and 0 comma 5 3x − y = 3p − q 3x + y = q − 3p x − y = p − q x + y = q − p

Answers: 1

Answer

Mathematics, 21.06.2019 21:00

Atorch and a battery cost 2.50 altogether.the torch costs 1.50 more than the battery.what fraction of the total price is the torch? give your answer in its simplest form.

Answers: 2

Answer

Mathematics, 21.06.2019 22:00

Determine which postulate or theorem can be used to prove that lmn =nmo

Answers: 3

Answer

Mathematics, 21.06.2019 23:30

An engineer scale model shows a building that is 3 inches tall. if the scale is 1 inch = 600 feet, how tall is the actual building?

Answers: 3

Answer

You know the right answer?

Nationwide survey of college seniors by the University of Michigan revealed that almost 70% disappro...