I need help with this

Taco Bell has decided to keep their doors open all night. There are 25 employees that have volunteered for the night shift. a) I

DIA [1.3K]

Answer:

a) 1,081,575

b) 735,471

c) 1,075,140

d) 0.3159

Step-by-step explanation:

a)

This is a combination of 25 elements taken 8 at a time

$\binom{25}{8}=\frac{25!}{8!(25-8)!}=\frac{25!}{8!17!}=1081575$

b)

Supposing number 1 is the best, if we leave him/her out we will now have 24 employees, so now it is a combination of 24 elements taken 8 at a time

$\binom{24}{8}=\frac{24!}{8!(24-8)!}=\frac{24!}{8!16!}=735471$

c)

Let's compute the complement of this set and then subtract.

That is to say, compute how many crews do not have any of the 10 best.

This would be a combination of 25-10 = 15 taken 8 at a time

$\binom{15}{8}=\frac{15!}{8!(15-8)!}=\frac{15!}{8!7!}=6435$

If we subtract this figure from the total of possible crews, we get 1,081,575 - 6,435 = 1,075,140 possible crews with at least one of the 10 best.

d)

From the figure obtained in c) we subtract the figure obtained in b) 1,075,140 - 735,471 = 339,669 and this is the number of crews that do not have number 1, so the probability that in a crew with at least one of the 10 best number 1 is not there is

339,669/1,075,140 = 0.3159

5 0

3 years ago

Let X be the damage incurred (in $) in a certain type of accident during a given year. Possible X values are 0, 1000, 5000, and

KengaRu [80]

Answer:

$150

Step-by-step explanation:

In this case, we have a random variable with four possible outcomes

0, 1000, 5000 and 10000

and four possible probabilities of occurrence

0.83, 0.10, 0.05 and 0.02

respectively.

The expectation of this random variable is (* means multiplication),

0.83*0 + 0.10*1000 + 0.05*5000 + 0.02*10000 = 100 + 250 + 200 = 550

This represents the amount of money the company expects to pay a customer in a given year.

As the deductible is $500, the customer would pay $500 in case of an accident, so the company would only have to pay

$550 - $500 = $50.

So, if the company wishes a profit of $100, the premium amount should be $150.

7 0

3 years ago

-3/5 (15x30) = 197 solve for x

Alekssandra [29.7K]

Answer:

X = 215/9

Step-by-step explanation:

- 3/5 * 5(3x + 6) = 197

-3 *(3x + 6) = 197

-9x - 18 = 197

- 9x = 197 + 18

X = - 215/9

6 0

4 years ago

A bicycle company is designing women's bicycle frames. The frames can accommodate any woman taller than 54.5 inches. Given that

ladessa [460]

Using the normal distribution, it is found that 0.13% of American women CAN NOT use the bicycles designed by this company.

<h3>What is Normal Probability Distribution?</h3>

The z-score of a measure X of a normally distributed variable with mean and standard deviation is given by:

$z=\dfrac{x-\mu}{\sigma}$

The z-score measures how many standard deviations the measure is above or below the mean.
Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

$\mu = 65\ \ \sigma= 3.5$

The proportion of women that cannot use the bikes(smaller than 54.5 inches) is the p-value of Z when X = 54.5, hence:

$z=\dfrac{x-\mu}{\sigma}$

$z = \dfrac{54.5-65}{3.5}$

Z = -3

Z = -3 has a p-value of 0.0013.

0.0013 = 0.13% of American women CAN NOT use the bicycles designed by this company.

More can be learned about the normal distribution at brainly.com/question/27850813

#SPJ1

4 0

2 years ago

The heights of american men aged 18 to 24 are approximately normally distributed with a mean of 68 inches and standard deviation

Rudik [331]

A normal distribution is symmetrical about the mean. Therefore half of all young men are shorter than 68 inches.

7 0

4 years ago

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