10+(-3.5)x2+(-9)/(-3)

7.109) The leading brand of dishwasher detergent has a 30% market share. A sample of 25 dishwasher detergent customers was taken

Rina8888 [55]

Answer:

0.9021 = 90.21% probability that 10 or fewer customers choose the leading brand

Step-by-step explanation:

For each customer, there are only two possible outcomes. Either they choose the leading brand, or they do not. The probability of a customer choosing the leading brand is independent of any other customer, which 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.

The leading brand of dishwasher detergent has a 30% market share.

This means that $p = 0.3$

A sample of 25 dishwasher detergent customers was taken.

This means that $n = 25$

a. What is the probability that 10 or fewer customers choose the leading brand?

This is:

$P(X \leq 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)$

In which

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

$P(X = 0) = C_{25,0}.(0.3)^{0}.(0.7)^{25} = 0.0001$

$P(X = 1) = C_{25,1}.(0.3)^{1}.(0.7)^{24} = 0.0014$

$P(X = 2) = C_{25,2}.(0.3)^{2}.(0.7)^{23} = 0.0074$

$P(X = 3) = C_{25,3}.(0.3)^{3}.(0.7)^{22} = 0.0243$

$P(X = 4) = C_{25,4}.(0.3)^{4}.(0.7)^{21} = 0.0572$

$P(X = 5) = C_{25,5}.(0.3)^{5}.(0.7)^{20} = 0.1030$

$P(X = 6) = C_{25,6}.(0.3)^{6}.(0.7)^{19} = 0.1472$

$P(X = 7) = C_{25,7}.(0.3)^{7}.(0.7)^{18} = 0.1712$

$P(X = 8) = C_{25,8}.(0.3)^{8}.(0.7)^{17} = 0.1651$

$P(X = 9) = C_{25,9}.(0.3)^{9}.(0.7)^{16} = 0.1336$

$P(X = 10) = C_{25,10}.(0.3)^{10}.(0.7)^{15} = 0.0916$

Then

$P(X \leq 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0001 + 0.0014 + 0.0074 + 0.0243 + 0.0572 + 0.1030 + 0.1472 + 0.1712 + 0.1651 + 0.1336 + 0.0916 = 0.9021$

0.9021 = 90.21% probability that 10 or fewer customers choose the leading brand

3 0

2 years ago

Solve this following system by graphing <br> X-y=4<br> X+y=2

OverLord2011 [107]

Answer:

The answer is x = 3 and y = -1

Step-by-step explanation:

If you were to graph the two lines, their equations would be y = x - 4 and y = -x + 2. The two lines intersect at the point (3, -1), so the solution to the system is x = 3 and y = -1.

5 0

2 years ago

A store manager is accepting applications for part-time workers. he can hire no more than 14 people. so far,he has hired 9 peopl

Lorico [155]

The manager already hired 9 people. Let $x$ be the number of people he still can hire. Since these people will add to the 9 he already hired, when the hiring campaign will be over he will have hired $9+x$ people. We know that he can't hire more than 14 people, so the number of people hired must be less than or equal to 14:

$9+x \leq 14$

If we subtract 9 from both sides, we have

$x \leq 14-9=5$

so, the manager can hire at most 5 other people

6 0

3 years ago

A rectangle has an area of 96 cm2 The length of the rectangle is 4 cm longer than the width. Work out the length and width of th

Svetach [21]

Area of a rectangle: 2(L+W)
length: 4+W

Area: 2(4+W) + 2W = 96
8+2W+2W = 96
8+4W = 96
4W = 88
W= 22cm

Calculate for length: 2L + 2(22) = 96
2L + 44 = 96
2L = 52
L = 26cm

• The length is 26cm and width is 22 cm.

3 0

3 years ago

Ramona wants to buy cheese pizza for her family and friends gathering. She stop by nine wonder pizza and figures out that they h

Kryger [21]

Answer:

Large cheese

Step-by-step explanation:

The large cheese because it's two more dollars than the medium and she has a lot of people gathering

6 0

2 years ago

Read 2 more answers