Description
Week 5: Normal Distribution
Week | Assignments | Due Date |
Week 5 | Graded Discussion | Suggested Due Date—
Initial Post: Wednesday of Week 5
Due Date— Responses: Sunday of Week 5 [Have two posts on two different days] |
Knewton Homework Assignments
Understanding Normal Distribution Applications of the Normal Distribution – Excel Central Limit Theorem for Means Central Limit Theorem for Proportions Probability Using the Normal Distribution Understanding the Empirical Rule |
Sunday of Week 5 |
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Week 5 Assignment – Applications of the Normal Distribution – Excel
Activity 1
Question
The number of miles a motorcycle, X, will travel on one gallon of gasoline is modeled by a normal distribution with mean 44 and standard deviation 5. If Mike starts a journey with one gallon of gasoline in the motorcycle, find the probability that, without refueling, he can travel more than 50 miles.
Round your answer to four decimal places.
Answer
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Activity 2
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.
Answer
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Activity 3
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.
Answer
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Activity 4
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 2.5% 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.
Answer
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Activity 5
Question
In a survey of men aged 20-29 in a country, the mean height was 73.4 inches with a standard deviation of 2.7 inches. Find the minimum height in the top 10% of heights.
Answer
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Activity 6
Question
Two thousand students took an exam. The scores on the exam have an approximate normal distribution with a mean of μ=81 points and a standard deviation of σ=4 points. The middle 50% of the exam scores are between what two values?
Answer
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Activity 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.
Answer
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Activity 8
Question
A worn, poorly set-up machine is observed to produce components whose length X follows a normal distribution with mean 14 centimeters and variance 9. Calculate the probability that a component is at least 12 centimeters long.
Answer
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Activity 9
Question
Sugar canes have lengths, X, that are normally distributed with mean 365.45 centimeters and standard deviation 4.9 centimeters. What is the probability of the length of a randomly selected cane being between 360 and 370 centimeters?
Answer
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Activity 10
Question
Suppose that the weight, X, in pounds, of a 40-year-old man is a normal random variable with mean 147 and standard deviation 16. Calculate P(120≤X≤153).
Answer
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Activity 11
Question
A tire company finds the lifespan for one brand of its tires is normally distributed with a mean of 47,500 miles and a standard deviation of 3,000 miles. What mileage would correspond to the highest 3% of the tires?
Answer
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Activity 12
Question
A firm’s marketing manager believes that total sales for next year will follow the normal distribution, with a mean of $3.2 million and a standard deviation of $250,000. Determine the sales level that has only a 3% chance of being exceeded next year.
Answer
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