Can somebody help me on this problem please I will give you brainliest:)

The mean annual cost of an automotive insurance policy is normally distributed with a mean of $1140 and standard deviation of $3

DerKrebs [107]

Using the normal distribution, it is found that the probabilities are given as follows:

a) 0.8871 = 88.71%.

b) 0.0778 = 7.78%.

c) 0.8485 = 84.85%.

<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.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

The parameters in this problem are given as follows:

$\mu = 1140, \sigma = 310, n = 16, s = \frac{310}{\sqrt{16}} = 77.5$

Item a:

The probability is the p-value of Z when X = 1250 subtracted by the p-value of Z when X = 1000, hence:

X = 1250:

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

By the Central Limit Theorem

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

$Z = \frac{1250 - 1140}{77.5}$

Z = 1.42

Z = 1.42 has a p-value of 0.9222.

X = 1000:

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

$Z = \frac{1000 - 1140}{77.5}$

Z = -1.81

Z = -1.81 has a p-value of 0.0351.

0.9222 - 0.0351 = 0.8871 = 88.71% probability.

Item b:

The probability is one subtracted by the p-value of Z when X = 1250, hence:

1 - 0.9222 = 0.0778 = 7.78%.

Item c:

The probability is the p-value of Z when X = 1220, hence:

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

$Z = \frac{1220 - 1140}{77.5}$

Z = 1.03

Z = 1.03 has a p-value of 0.8485.

0.8485 = 84.85% probability.

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

#SPJ1

3 0

2 years ago

Hey motorcycle shop maintains an inventory of four times as many new bikes as used bikes. If there are 16 new bikes how many use

nlexa [21]

Motorcycle shop maintains

U - used bikes
N - new bikes = 4N

1 U = 4N
? U = 16 new bikes

16/4 = 4. There are 4 used bikes that are in stock.

7 0

4 years ago

Read 2 more answers

Find the area: (I will give brainliest) +50 points.

scZoUnD [109]

Answer:

$A_{total} = 16\ cm^2$

Step-by-step explanation:

Step 1: Determine the area of the top rectangle

We can tell that the total shape seems like two rectangles glued together. We can separate the top rectangle and determine the area of it and then determine the area of the bottom rectangle and combine them. Lets first solve the left rectangle.

$A=l*w$

$A_{top\ rectangle}=6\ cm * 2\ cm$

$A_{top\ rectangle}=12\ cm^2$

Step 2: Determine the area of the bottom rectangle

$A=l*w$

$A_{bottom\ rectangle}=2\ cm * 2\ cm$

$A_{bottom\ rectangle}=4\ cm^2$

Step 3: Determine the total area

$A_{total}=A_{top\ rectangle}+A_{bottom\ rectangle}$

$A_{total}=12\ cm^2+4\ cm^2$

$A_{total} = 16\ cm^2$

Answer: $A_{total} = 16\ cm^2$

8 0

2 years ago

Read 2 more answers

Colby wants to set square tiles on the top of a wooden box. The top of the box is a rectangle 7 1/2 inches long and 5 1/2 inches

Sever21 [200]

You will need 82 1/4 1/2 tiles and 165 1/4 tiles

8 0

3 years ago

Find (f ° g)(0). *

atroni [7]

Answer:

B

Step-by-step explanation:

Remark

I have to represent f(x) as plus +f(x)

I like to show this situation as +f(g(x)) which I think is much clearer.

+f(x) = 5x - 4

Solution

+f(g(x)) = 5(g(x)) - 4 What has happened is that wherever you see an x on the right you put in g(x).

Now on the right, you put whatever g(x) is equal to.

+f(g(x)) = 5(x^2 - 1) - 4

Remove the brackets.

+f(g(x)) = 5x^2 - 5 - 4

And make x = 0

+f(g(0)) = 5*0 - 5 - 4

+f(g(0)) = - 9

8 0

3 years ago