Question

1. Assume that the weights of a particular group of men follow approximately a normal distribution with a mean of 168.7 pounds and a standard deviation of 13.5 pounds. Use built-in functions of your calculator (write down what you entered in one line) or Table A.2. to answer the following questions. No credit if you use the Rule covered in Chapter 7. Show your work to receive credit. Clearly state the answer. a) What percent weigh between 160 and 190 pounds? Round to two decimal places, if needed. b) What percent weigh less than 170.5 pounds? Round to two decimal places, if needed. c) What is the area to the left of 165 pounds? Provide the answer as a percent. Round to two decimal places, if needed. d) To be in a certain club, a man needs to be in the bottom 8% of weights. What weight qualifies for a club membership? Round to one decimal place, if needed. e) What percent weigh more than 150 pounds? Round to two decimal places, if needed. f) To qualify for a certain program, a man needs to be in the top 12% of weights. What weight qualifies for the program? Round to one decimal place, if needed. 2. Use the 68-95-97.5 Rule covered in Chapter 7. No credit if you use z-scores or other methods. Show your work to receive credit. Clearly state the answer. Each month, am American household generates an average of 28 pounds of garbage and recycling. Assume that the standard deviation is 1.5 pounds. If a household is selected at random, find the percentage of it generating a) Between 26.5 and 32.5 pounds per month? Round to four decimal places, if needed. Draw the figure and shade the region. b) More than 31 pounds per month? Round to four decimal places, if needed. Draw the figure and shade the region. c) Let X be the amount of garbage and recycling generated per month by one household. Find the probability P(23.5<x<25). Draw the figure and shade the region.

Answer 1

Sorry as per the HOMEWORKLIB RULES I'm only allowed to solve the first question

1)

This is a normal distribution question with

a) P(160.0 < x < 190.0)=?

This implies that

P(160.0 < x < 190.0) = P(-0.6444 < z < 1.5778) = P(Z < 1.5778) - P(Z < -0.6444)

P(160.0 < x < 190.0) = 0.94269421807713 - 0.259658042272917

b) P(x < 170.5)=?

The z-score at x = 170.5 is,

z = 0.1333

This implies that

c) Given in the question

P(X < x) = 0.08

This implies that

P(Z < -1.4051) = 0.08

With the help of formula for z, we can say that

x = 149.7

d) P(x > 150.0)=?

The z-score at x = 150.0 is,

z = -1.3852

This implies that

P(x > 150.0) = P(z > -1.3852) = 1 - 0.08299566035950795

e) Given in the question

P(X > x) = 0.12

1 - P(X > x) = 1 - 0.12

P(X < x) = 0.88

This implies that

P(Z < 1.175) = 0.88

With the help of formula for z, we can say that

x = 184.6

PS: you have to refer z score table to find the final probabilities.

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