(ANSWER) MATH 225N WEEK 5 ASSIGNMENT: APPLICATIONS OF THE NORMAL DISTRIBUTION - EXCEL - Essay Prowess
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# (ANSWER) MATH 225N WEEK 5 ASSIGNMENT: APPLICATIONS OF THE NORMAL DISTRIBUTION – EXCEL

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## Question

The weights of bags of raisins are normally distributed with a mean of 175 grams and a standard deviation of 11 grams. Bags in the upper 4.5% are too heavy and must be repackaged. Also, bags in the lower 5% do not meet the minimum weight requirement and must be repackaged.

What are the ranges of weights for raisin bags that need to be repackaged?   Use Excel, and round your answers to the nearest integer.

Question 2

## Question

A worn, poorly set-up machine is observed to produce components whose length X follows a normal distribution with a mean equal to 14 centimeters and a variance equal to 9.

Determine the probability that a component is at least 12 centimeters long.  Round your answer to four decimal places.

Question 3

## Question

A certain type of mango that weighs over 425 grams is considered to be large in size. The weights for this type of mango, X grams, are normally distributed with a mean of 400 and a standard deviation of 25.

Find the probability that a randomly selected mango of this type will not be considered as large size.  Round your answer to four decimal places.

Question 4

The top 5% of applicants on a test will receive a scholarship. If the test scores are normally distributed with a mean of 76 and a standard distribution of 12, what is the lowest test score that still qualifies for a scholarship?

Question 5

The average speed of a car on the highway is 72 miles per hour with a standard deviation of 5.2 miles per hour. Assume the speed of the car, X, is normally distributed.

Find the probability that the speed is less than 60 miles per hour.  Round your answer to four decimal places.

Question 6.

A worn, poorly set-up machine is observed to produce components whose length X follows a normal distribution with a mean equal to 14 centimeters and a variance equal to 9.

Determine the probability that a component is at least 10 centimeters long.  Round your answer to four decimal places.

Question 7

## Question

On average, 28 percent of 18 to 34 year olds check their social media profiles before getting out of bed in the morning. Suppose this percentage follows a normal distribution with a random variable X, which has a standard deviation of five percent.

Find the probability that the percent of 18 to 34 year olds who check social media before getting out of bed in the morning is, at most, 32.  Round your answer to four decimal places.

Question 8

## Question

A credit card company receives numerous phone calls throughout the day from customers reporting fraud and billing disputes. Most of these callers are put “on hold” until a company operator is free to help them. The company has determined that the length of time a caller is on hold is normally distributed with a mean of 2.5 minutes and a standard deviation 0.5 minutes.

If 1.5% of the callers are put on hold for longer than x minutes, what is the value of x? Use Excel, and round your answer to two decimal places.

question 9

Question

Assume that the salaries of fast food restaurant managers are normally distributed with a mean of $48,000 and a standard deviation of$4,000.

What is the lowest amount that a manager needs to make and still be one of the top 7% earners?  Use Excel, and round your answer to the nearest dollar.