What are the defining properties of a parallelogram?

The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer ab

GarryVolchara [31]

Using the normal distribution, the probabilities are given as follows:

a) 0.6517 = 65.17%

b) 0.0823 = 8.23%.

c) 0.6109 = 61.09%.

<h3>Normal Probability Distribution</h3>

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

$Z = \frac{X - \mu}{\sigma}$

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:

$\mu = 8.9, \sigma = 2.8$

Item a:

The probability is the <u>p-value of Z when X = 10</u>, hence:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{10 - 8.9}{2.8}$

Z = 0.39

Z = 0.39 has a p-value of 0.6517.

0.6517 = 65.17% probability that the time is less than 10 minutes.

Item b:

The probability is the <u>one subtracted by the p-value of Z when X = 5</u>, hence:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{5 - 8.9}{2.8}$

Z = -1.39

Z = -1.39 has a p-value of 0.0823.

0.0823 = 8.23% probability that the time is more than 5 minutes.

Item c:

The probability is the <u>p-value of Z when X = 15 subtracted by the p-value of Z when X = 8</u>, hence:

X = 15:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{15 - 8.9}{2.8}$

Z = 2.18

Z = 2.18 has a p-value of 0.9854.

X = 8:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{8 - 8.9}{2.8}$

Z = -0.32

Z = -0.32 has a p-value of 0.3745.

0.9854 - 0.3745 = 0.6109 = 61.09%.

More can be learned about the normal distribution at brainly.com/question/4079902

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5 0

2 years ago

The Movie Haven is planning to order new medium-size popcorn containers. It has a choice of four different containers. It costs

Ksju [112]

Answer:

only option less than $3 is (C)

Step-by-step explanation:

Volume(cylinder) = πr²h or Bh

I used the guess-and-check method and got the following:

A) 3.85

B) 3.39

C) 2.67

D) 5.65

7 0

3 years ago

What fraction of the larger square has not been shaded?

____ [38]

A: 14/16 that is the answer

4 0

3 years ago

Please answer this correctly

irina [24]

Answer:

100%

Step-by-step explanation:

6 possibilities: 3 odd and 3 even

P(odd or even) 6/6= 100%

5 0

3 years ago

A monument in the shape of a right triangle sits on a rectangular pedestal that is 5 meters high by 11 meters long. The longest

Vladimir [108]

Based on the information given, there are 2 possibilities:
1) the hypotenuse is the base of the triangles, sitting on the rectangular pedestal
2) the right angle touches the pedestal, with the base equalling the pedestal length

In 1) it is pretty straightforward, because the right angle is the apex (top). The base is 61m, because the longest side in a right is always the hypotenuse.
So now we need the height (h), which will split the triangle into two 45-45-90 triangles with base and h = 30.5 (1/2 the initial base)
This will make the height off the ground = 30.5+5 = 35.5 m

2) with right angle touching the pedestal, we can only assume that the base equals the pedestal length, 11. Then we need the missing side (h), which we can derive from Pythagorean Theorem:
${h}^{2} = {61}^{2} - {11}^{2} \\ \sqrt{({h}^{2})} = \sqrt{({61}^{2} - {11}^{2})} \\ h = \sqrt{({61}^{2} - {11}^{2})} = \sqrt{(3721- 121)} \\ h= \sqrt{3600} = 60$
So in this triangle the height off ground would be 60+5 = 65 m

6 0

4 years ago