A 1000 watt microwave does --------- joules of work in 5 seconds

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

3 years ago

A group of 196 students needs to be seated in a square formation for a yearbook photo. How many students should be in each row?

givi [52]

Answer:

There should be a number of 14 students in each row

Step-by-step explanation:

Find the factors of 196 then find the Greatest factor pairs which give you the numbers of 14 and 14. Now you have your answer of 14 rows and 14 columns.

6 0

3 years ago

Someone needs to hear this. So here it is. God will pull you through. You just need to have faith. You just have to keep going.

vagabundo [1.1K]

Answer: thank you

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

The sales tax in your state is 5% if a car costs $24,600 what is the total cost including tax?

Svetach [21]

<h2>Greetings!</h2>

Answer:

$25830

Step-by-step explanation:

If 100% of the car price is 24,600 , then you can imagine that extra 5% being added to this

100 + 5 = 105

So you need to find what 105% of the cost was.

To do this you can use the percentage formula:

Amount x $\frac{percentage}{100}$

Now, you can simply plug the values into this

24,600 x $\frac{105}{100}$

24600 x 1.05 = 25830

<h3>So the total cost including tax would be $25830!</h3><h3 /><h2>Hope this helps!</h2>

7 0

3 years ago

SOMEONE PLEASE HELP ME

Ostrovityanka [42]

Answer:

28, 30, 32

Step-by-step explanation:

Three consecutive even numbers are three even numbers that are next to each other. For example, 2, 4 and 6 would be 3 consecutive even numbers.

With this sort of problem, you want to try to let each number be equal to one thing and then construct the same number of equations as you have variables:

Let's let,

Integer 1 = X

Integer 2 = Y

Integer 3 = Z

X + Y + Z = 90

We also know, that

Y = X + 2

And that

Z = X + 4

Now, we can sub these equations into the first equation. We do this so that we have everything represented as the same variable.

90 = X + (X+2) + (X+4)

90 = 3X + 6

84 = 3X

28 = X

So, the numbers are 28, 30 and 32

8 0

3 years ago