Question

Part 1.

3.13 Overweight baggage: Suppose weights of the checked baggage of airline passengers follow a nearly normal distribution with mean 44.8 pounds and standard deviation 3.3 pounds. Most airlines charge a fee for baggage that weigh in excess of 50 pounds. Determine what percent of airline passengers incur this fee. (Round to the nearest percent.) __________.

Part 2.

There are two distributions for GRE scores based on the two parts of the exam. For the verbal part of the exam, the mean is 151 and the standard deviation is 7. For the quantitative part, the mean is 153 and the standard deviation is 7.67. Use this information to compute each of the following:
(Round to the nearest whole number.)

a) The score of a student who scored in the 80-th percentile on the Quantitative Reasoning section. ________.
b) The score of a student who scored worse than 65% of the test takers in the Verbal Reasoning section. ________.

Part 3.

3.10 Heights of 10 year olds: Heights of 10 year olds, regardless of gender, closely follow a normal distribution with mean 56 inches and standard deviation 5 inches.

a) What is the probability that a randomly chosen 10 year old is shorter than 47 inches? (Keep 4 decimal places.) ____________.
b) What is the probability that a randomly chosen 10 year old is between 60 and 66 inches? (Keep 4 decimal places.) __________.
c) If the tallest 10% of the class is considered "very tall", what is the height cutoff for "very tall"? (Keep 2 decimal places.) ________. inches
d) The height requirement for Batman the Ride at Six Flags Magic Mountain is 55 inches. What percent of 10 year olds cannot go on this ride? (Keep 2 decimal places.) %_______.

Part 4.

3.12 Speeding on the I-5, Part I: The distribution of passenger vehicle speeds traveling on the Interstate 5 Freeway (I-5) in California is nearly normal with a mean of 72.1 miles/hour and a standard deviation of 5 miles/hour. (Keep 2 decimal places.)

a) What percent of passenger vehicles travel slower than 80 miles/hour? _________%
b) What percent of passenger vehicles travel between 60 and 80 miles/hour? ____________%
c) How fast do the fastest 5% of passenger vehicles travel? __________ miles/hour
d) The speed limit on this stretch of the I-5 is 70 miles/hour. Approximate what percentage of the passenger vehicles travel above the speed limit on this stretch of the I-5. __________%

Answer 1

Answer:

Part 1.

3.13 Overweight baggage: Suppose weights of the checked baggage of airline passengers follow a nearly normal distribution with mean 44.8 pounds and standard deviation 3.3 pounds. Most airlines charge a fee for baggage that weigh in excess of 50 pounds. Determine what percent of airline passengers incur this fee. (Round to the nearest percent.) __________.

Z value for 50, z =(50-44.8)/3.3 =1.58

P( x >50) = P(z >1.58) =0.0571

The required percentage = 5.71%

=6% ( rounded)

Part 2.

There are two distributions for GRE scores based on the two parts of the exam. For the verbal part of the exam, the mean is 151 and the standard deviation is 7. For the quantitative part, the mean is 153 and the standard deviation is 7.67. Use this information to compute each of the following:
(Round to the nearest whole number.)

a).The score of a student who scored in the 80-th percentile on the Quantitative Reasoning section.

Z value for 80^th percentile =0.842

The required score = mean+z*sd = 153+0.842*7.67 =159.45814

=159 ( rounded)

b) The score of a student who scored worse than 65% of the test takers in the Verbal Reasoning section.

Z value for 65^th percentile = 0.385

The required score = mean+z*sd = 151+0.385*7 =153.695

=154 ( rounded)

Part 3.

3.10 Heights of 10 year olds: Heights of 10 year olds, regardless of gender, closely follow a normal distribution with mean 56 inches and standard deviation 5 inches.

a) What is the probability that a randomly chosen 10 year old is shorter than 47 inches? (Keep 4 decimal places.) ____________.

z value for 47, z =(47-56)/5 = -1.8

P( x <47) = P( z < -1.8)

= 0.0359

b) What is the probability that a randomly chosen 10 year old is between 60 and 66 inches? (Keep 4 decimal places.) __________.

z value for 60, z =(60-56)/5 = 0.8

z value for 66, z =(66-56)/5 = 2

P( 60<x<66) = p( 0.8<z<2) =P( z <2) –P(z < 0.8)

=0.9772-0.7881

=0.1891

c) If the tallest 10% of the class is considered "very tall", what is the height cutoff for "very tall"? (Keep 2 decimal places.) ________. inches
z value for top 10% is 1.282

the required score = mean+z*sd = 56+1.282*5

=62.41 inches

d) The height requirement for Batman the Ride at Six Flags Magic Mountain is 55 inches. What percent of 10 year olds cannot go on this ride? (Keep 2 decimal places.) %_______.

z value for 55, z =(55-56)/5 = -0.2

P( x <55) = P( z < -0.2)= 0.4207

The required percentage = 42.07%

Part 4.

3.12 Speeding on the I-5, Part I: The distribution of passenger vehicle speeds traveling on the Interstate 5 Freeway (I-5) in California is nearly normal with a mean of 72.1 miles/hour and a standard deviation of 5 miles/hour. (Keep 2 decimal places.)

a) What percent of passenger vehicles travel slower than 80 miles/hour? _________%
z value for 80, z =(80-72.1)/5=1.58

P( x<80) = P( z <1.58) = 0.9429

The required percentage = 94.29%

b) What percent of passenger vehicles travel between 60 and 80 miles/hour? ____________%

z value for 60, z =(60-72.1)/5=-2.42

z va lue for 80, z =(80-72.1)/5=1.58

P( 60<x<80) = P( -2.42<z<1.58) = P(z < 1.58)-P(z <-2.42)

=0.9429- 0.0078

=0.9351

The required percentage = 93.51%

c) How fast do the fastest 5% of passenger vehicles travel? __________ miles/hour

z value for top 5% = 1.645

x= mean+z*sd = 72.1+1.645*5=80.325

= 80.33 miles/hour

d) The speed limit on this stretch of the I-5 is 70 miles/hour. Approximate what percentage of the passenger vehicles travel above the speed limit on this stretch of the I-5. __________%

z value for 70, z =(70-72.1)/5=-0.42

P( x> 70) = P( z > -0.42) = 0.6628

The required percentage = 66.28%

Note: Probability values are used to calculate excel function: =NORM.S.DIST(z,TRUE)