Q1
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.
Q2
The top 5% of applicants on a test will receive a scholarship. If the test scores are normally distributed with a mean of 600 and a standard distribution of 85, how low can an applicant score to still qualify for a scholarship?
Use Excel, and round your answer to the nearest integer
Q3
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.
Q4
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.
- Round your answer to four decimal places.
Q5
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.
Q6
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).
- Round your answer to four decimal places.
Q7
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.
Q8
A group of students with normally distributed salaries earn an average of $6,800 with a standard deviation of $2,500. Find the cutoff for the salary that corresponds to the lower 25% of all salaries. Use Excel, and round your answer to the nearest integer.
Q9
The average price of a laptop is $965. Assume laptop prices are approximately normally distributed with a standard deviation of $100. The least expensive 5% of laptops cost less than what amount?
- Use Excel, and round your answer to two decimal places.
Q10
The weights of oranges are normally distributed with a mean of 12.4 pounds and a standard deviation of 3 pounds. Find the minimum value that would be included in the top 5% of orange weights.
- Use Excel, and round your answer to one decimal place.
Q11
The number of walnuts in a mass-produced bag is modeled by a normal distribution with a mean of 44 and a standard deviation of 5. Find the number of walnuts in a bag that has more walnuts than 80% of the other bags.
- Use Excel, and round your answer to the nearest integer.
Q12
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.
- Use Excel, and round your answer to one decimal place.
Q13
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.
- Use Excel, and round your answer to the nearest dollar.
Q14
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?
- Use Excel, and round your answers to the nearest integer.
Solution
Q1
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.
Ans:
Repackaging has to be done if the weights are less than 1 grams and more than 2 grams.
Correct answers:
- 157
- 194
Q2
The top 5% of applicants on a test will receive a scholarship. If the test scores are normally distributed with a mean of 600 and a standard distribution of 85, how low can an applicant score to still qualify for a scholarship?
Use Excel, and round your answer to the nearest integer
Ans: 740……………please follow the link below to purchase all the solutions at just $5
