When redesigning the ejection seat, which probability is more relevant?

1.

Student: Karlene Neil Date: 11/29/18

Instructor: Richard Naccarato Course: MAT2058 Statistics SU01

Assignment: Week 3 Homework

1: Standard Normal Table (Page 1)

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

Click to view page 1 of the table. Click to view page 2 of the table.1 2

.The area of the shaded region is 0.8106

(Round to four decimal places as needed.)

z = 0.88

2: Standard Normal Table (Page 2)

2. Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

0

.The indicated z score is − 0.81

(Round to two decimal places as needed.)

z

0.2090

3.

3: Standard Normal Table (Page 1)

Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

Click to view page 1 of the table. Click to view page 2 of the table.3 4

. The area of the shaded region is (Round to four decimal places as needed.)0.1587

85

4: Standard Normal Table (Page 2)

4. Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

. The area of the shaded region is (Round to four decimal places as needed.)0.2805

108 132

5.

5: Standard Normal Table (Page 1)

Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

Click to view page 1 of the table. Click to view page 2 of the table.5 6

The indicated IQ score, . x, is (Round to one decimal place as needed.)96.2

x

0.6

6: Standard Normal Table (Page 2)

6.

7.

8.

A survey found that women's heights are normally distributed with mean in. and standard deviation in. The survey also found that men's heights are normally distributed with a mean . in. and standard deviation Complete parts a through c below.

62.7 2.8 67.9 2.9

a. Most of the live characters at an amusement park have height requirements with a minimum of 4 ft in. and a maximum of 6 ft in. Find the percentage of women meeting the height requirement.

8 4

%.The percentage of women who meet the height requirement is 99.16

(Round to two decimal places as needed.)

b. Find the percentage of men meeting the height requirement.

%.The percentage of men who meet the height requirement is 99.74

(Round to two decimal places as needed.)

c. If the height requirements are changed to exclude only the tallest 5% of men and the shortest 5% of women, what are the new height requirements?

The new height requirements are at least in. and at most in.58.1 72.7

(Round to one decimal place as needed.)

Which of the following is NOT a property of the sampling distribution of the sample mean?

Choose the correct answer below.

A. The sample means target the value of the population mean.

B. The expected value of the sample mean is equal to the population mean.

C. The mean of the sample means is the population mean.

D. The distribution of the sample mean tends to be skewed to the right or left.

Assume that women's ,heights are normally distributed with a mean given by and a standard deviation given by .

μ = 62.4 in σ = 1.7 in (a) If 1 woman is randomly selected, find the probability that her height is less than in.63 (b) If women are randomly selected, find the probability that they have a mean height less than in.31 63

(a) . The probability is approximately 0.6379

(Round to four decimal places as needed.)

(b) .The probability is approximately 0.9753

(Round to four decimal places as needed.)

9.

10.

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between lb and lb. The new population of pilots has normally distributed weights with a mean of and a standard deviation of

.

150 201 156 lb

31.5 lb

a. If a pilot is randomly selected, find the probability that his weight is between lb and lb.150 201

. The probability is approximately (Round to four decimal places as needed.)0.4990

b. If different pilots are randomly selected, find the probability that their mean weight is between lb and lb.36 150 201

. The probability is approximately (Round to four decimal places as needed.)0.8735

c. When redesigning the ejection seat, which probability is more relevant?

A. Part (a) because the seat performance for a sample of pilots is more important.

B. Part (a) because the seat performance for a single pilot is more important.

C. Part (b) because the seat performance for a single pilot is more important.

D. Part (b) because the seat performance for a sample of pilots is more important.

If ,and estimate nwith pand by using the normal distribution as an approximation to the binomial distribution; np 5 if nq 5,or then state that the normal approximation is not suitable.

np ≥ 5 nq ≥ 5 P(fewer than 5) = 13 = 0.5 < <

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. P(fewer than 5) = 0.1334

(Round to four decimal places as needed.)

B. The normal approximation is not suitable.

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