1)Heights of American Adult Males Are Normally Distributed with a Mean of 68.3 and a Standard

1)Heights of American Adult Males Are Normally Distributed with a Mean of 68.3 and a Standard

HW Quiz 5NAME:______BLOCK: _____

1)Heights of American adult males are normally distributed with a mean of 68.3” and a standard dev. of 2.9”

  1. Sketch the normal model below.
  1. What is the probability that you meet a male who is taller than 73”?P(X > 73) = 0.0525
  1. What is the chance that a male is between 5 and 6 feet tall?P(60 < X < 72) = 0.8969
  1. What percent of males are shorter than 5’6”?P(X < 66) = 0.2139
  1. The tallest 15% of men are above what height?P(X > A) = 0.15ORP(X < A) = 0.85

A = 71.306 inches

  1. What is the IQR of the heights?

P(X < Q1) = 0.25P(X < Q3) = 0.75

Q1 = 66.34 inQ3 = 70.26 inIQR = 3.92 in

2)A certain California road has a speed limit of 30 mph. However speeds of the cars driving on that road were recorded and found to have a mean of 34.65 mph and a standard deviation of 3.21 mph.

  1. The police decide that a car going 2.5 standard deviations above average should be pulled over and issued a ticket. What speed would this correspond to? (What is the minimum speed that would get a ticket?)

X = 42.675 mph

  1. What would be more unusual: a car traveling 44 mph on this road or a car traveling 25 mph on a road with an average speed of 33.17 mph and standard deviation of 2.36 mph?

This road:Other road:The car traveling 25 mph is more unusual.

= 2.913 = -3.462It is more standard deviations away from its

mean than the car traveling 44 mph is from its.

3)A machine is supposed to cut pieces of wood to a length of 12 inches. However the machine is not perfect. The company believes that the lengths can be described by a Normal model with a standard deviation of 0.36 inches. For quality control purposes, the company’s lawyers insist that no more than 3% of the lengths be shorter than 11 inches. What thickness (average) would the operators need to set the machine to so that they could achieve this goal?