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The average life of a certain type of small motor is 10 years with a standard deviation of 2 years. The manufacturer replaces free all motors that fail while under guarantee. If she is willing to replace only 3% of the motors that fail, how long a guarantee should be offered? Assume that the lifetime of a motor follows a normal distribution.

Answers

Answer 1

Answer:

Answer:

A guarantee of 6.24 years should be offered.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 10, \sigma = 2$

If she is willing to replace only 3% of the motors that fail, how long a guarantee should be offered?

The 3rd percentile, that is, the value of X when Z has a pvalue of 0.03. So X when Z = -1.88.

$Z = (X - \mu)/(\sigma)$

$-1.88 = (X - 10)/(2)$

$X - 10 = -1.88*2$

$X = 6.24$

A guarantee of 6.24 years should be offered.

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The original cost of an item is $64 but you have to pay $78.08. What is the markup of the item as a percent

Answers

Answer:

22%

Step-by-step explanation:

$78.08 - $64 = $14.08

$14.08 * 100% / $64 = 22%

Question 3 of 5A basketball has a radius of 4.5 inches. If the
ball is filled with 350 cubic inches of air, how
much more air is needed to fill it completely?
Round to the nearest whole number.

Answers

Answer:

32 cubic inches of air are needed to fill it completely.

Step-by-step explanation:

A basketball has the format of a sphere.

The volume of a sphere with radius r is given by the following equation:

$V = (4\pi r^(3))/(3)$

In this question:

Radius of 4.5 inches. So the volume, in cubic inches, is:

$V = (4\pi*(4.5)^(3))/(3) = 382$

The volume of the ball is 382 cubic inches.

350 cubic inches have already been filled.

So 382-350 = 32 cubic inches of air are needed to fill it completely.

CAN SOMEONE HELP PLEASE ASAP!!! ILL MAKE YOU BRAINLIEST

Answers

Answer:

I think the answer is D but I'm not 100 percent sure. I hope this helps

Step-by-step explanation:

I think I took this test before

18% of the cars in the parking lot are blue.If there are 150 cars in the parking lot,how many cars are blue

Answers

Answer:

Step-by-step explanation:

Software to detect fraud in consumer phone cards tracks the number of metropolitan areas where calls originate each day. It is found that 1% of the legitimate users originate calls from two or more metropolitan areas in a single day. However, 30% of fraudulent users originate calls from two or more metropolitan areas in a single day. The proportion of fraudulent users is 0.01%. If the same user originates calls from two or more metropolitan areas in a single day, what is the probability that the user is fraudulent?

Answers

Answer:

the probability that the user is fraudulent is 0.00299133

Step-by-step explanation:

Let be the events be:

G: The user generates calls from two or more areas.

NG: The user does NOT generate calls from two or more areas.

L: The user is legitimate.

F: The user is fraudulent.

The probabilities established in the statement are:

$P (G | L) = 0.01//P (G | F) = 0.30//P (F) = 0.0001//P (L) = 0.9999//$

With these values, the probability that a user is fraudulent, if it has originated calls from two or more areas is:

$((0.0001)(0.30))/((0.0001)(0.30)+(0.9999)(0.01)) = 0.00299133$

APEX. I’ll make you the brainliest . I need this ASAP :(Part 2: Use the formula you selected in part 1 to find the area of a circle with diameter 8 feet. Show your work and round your answer to the nearest hundredth. (2 points)
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Part 3: Use the formula you selected in Part 1 to find the area of a circle with diameter 10 feet. Show your work and round your answer to the nearest hundredth. (2 points)
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Part 4: Find the difference of your answers from part 2 and 3 to find the difference in the areas. Show your work and round your answer to the nearest hundredth. (1 point)

Answers

Answer:

Part 1= Pi * R Squared

Part 2: 50.27

Part 3: 78.54

Part 4: 28.27

Step-by-step explanation:

Part 1: Memorize the formula

Part 2: 8 feet diameter = Pi * 4 squared. 8 feet is the diameter so the radius is 4. 4 squared is 16. 16 * pi = approximately 50.27, but is 50.24 if 3.14 is used as pi.

Part 3: Pi * 5 squared since 10 is diameter. 25 * pi which is close to 78.54, but is 78.5 is 3.14 is used for pi.

Part 4: I subtracted Part 3 from Part 2.

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