Question

Suppose that an airline uses a seat width of 17.4 in. Assume men have hip breadths...

Suppose that an airline uses a seat width of 17.4 in. Assume men have hip breadths that are normally distributed with a mean of 14.9 in. and a standard deviation of 1 in. Complete parts​ (a) through​ (c) below.

​(a) Find the probability that if an individual man is randomly​ selected, his hip breadth will be greater than 17.4 in. The probability is ________. ​(Round to four decimal places as​ needed.)

​(b) If a plane is filled with 120 randomly selected​ men, find the probability that these men have a mean hip breadth greater than 17.4 in. The probability is ______ ​(Round to four decimal places as​ needed.) ​

(c) Which result should be considered for any changes in seat​ design: the result from part​ (a) or part​ (b)?

The result from ▼ part (b) OR part (a) should be considered because ▼ only average individuals should be considered OR the seats are occupied by individuals rather than means.

Homework Answers

Answer #1

µ = 14.9, σ = 1

a) P(X > 17.4) =

= P( (X-µ)/σ > (17.4-14.9)/1)

= P(z > 2.5)

= 1 - P(z < 2.5)

Using excel function:

= 1 - NORM.S.DIST(2.5, 1)

= 0.0062

b)

µ = 14.9, σ = 1, n = 120

P(X̅ > 17.4) =

= P( (X̅-μ)/(σ/√n) > (17.4-14.9)/(1/√120) )

= P(z > 27.3861)

= 1 - P(z < 27.3861)

Using excel function:

= 1 - NORM.S.DIST(27.3861, 1)

= 0.0000

c) The result from part (b) should be considered because only average individuals should be considered.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Suppose that an airline uses a seat width of 16.5 in. Assume men have hip breadths...
Suppose that an airline uses a seat width of 16.5 in. Assume men have hip breadths that are normally distributed with a mean of 14.6 in. and a standard deviation of 1 in. Complete parts​ (a) through​ (b) below. ​(a) Find the probability that if an individual man is randomly​ selected, his hip breadth will be greater than 16.5 in. The probability is ​(Round to four decimal places as​ needed.) ​(b) If a plane is filled with 126 randomly selected​...
Suppose that an airline uses a seat width of 16.1 in. Assume men have hip breadths...
Suppose that an airline uses a seat width of 16.1 in. Assume men have hip breadths that are normally distributed with a mean of 14.4 and a standard deviation of 1 inch. A. Find the probabulity that if an individual man is randomly selected his his will be greater than 16.1 B. If a plane is filled with 129 randomly selected men, find the probability that these men have a hip breadth greater than 16.1 C. Which result should be...
Suppose that an airline uses a seat width of 16.8  in. Assume men have hip breadths that...
Suppose that an airline uses a seat width of 16.8  in. Assume men have hip breadths that are normally distributed with a mean of 14.6 in. and a standard deviation of 1.1 in. Complete parts​ (a) through​ (c) below. ​(a) Find the probability that if an individual man is randomly​ selected, his hip breadth will be greater than 16.8 in. The probability is ​(Round to four decimal places as​ needed.)
Suppose that an airline uses a seat width of 16.9 in. Assume men have hip breadths...
Suppose that an airline uses a seat width of 16.9 in. Assume men have hip breadths that are normally distributed with a mean of 14.7 in. and a standard deviation of 1 in. Complete parts​ (a) through​ (c) below. ​(a) Find the probability that if an individual man is randomly​ selected, his hip breadth will be greater than 16.9 in. The probability is (b) If a plane is filled with 130 randomly selected​ men, find the probability that these men...
1. Assume that adults have IQ scores that are normally distributed with a mean of 104.3...
1. Assume that adults have IQ scores that are normally distributed with a mean of 104.3 and a standard deviation of 23.8. Find the probability that a randomly selected adult has an IQ greater than 147.0. The probability that a randomly selected adult from this group has an IQ greater than 147.0 is.. 2. Engineers want to design seats in commercial aircraft so that they are wide enough to fit 90​% of all males.​ (Accommodating 100% of males would require...
Central Limit Theorem 8. Designing Motorcycle Helmets. Engineers must consider the breadths of male heads when...
Central Limit Theorem 8. Designing Motorcycle Helmets. Engineers must consider the breadths of male heads when designing motorcycle helmets. Men have head breadths that are normally distributed with a mean of 6.0 inches and a standard deviation of 1.0 inches (based on anthropometric survey data from Gordon, Churchill, et al.) a) If one male is randomly selected, find the probability that his head breadth is less than 6.2 inches. b) The Safeguard Helmet Company plans an initial production run of...
Assume that the population of weights of men is normally distributed with mean 172 lb and...
Assume that the population of weights of men is normally distributed with mean 172 lb and standard deviation 29 lb. a. If an individual man is randomly selected, find the probability that his weight will be greater than 175 lb. (Round to four decimal places as needed.) b. Find the probability that 20 randomly selected men will have a mean weight that is greater than 175 lb. (Round to four decimal places as needed.) show work
Southwest airlines uses a boeing 737 for some of its flights and that aircraft seats 122...
Southwest airlines uses a boeing 737 for some of its flights and that aircraft seats 122 passengers. if the plane is full with 122 randomly selected men find the probabability that these men have a mean hip breadth greater than 17 inches.
Assume that the population of weights of men is normally distributed with mean 172 lb and...
Assume that the population of weights of men is normally distributed with mean 172 lb and standard deviation 29 lb. a. If an individual man is randomly selected, find the probability that his weight will be greater than 175 lb. (Round to four decimal places as needed.) b. Find the probability that 20 randomly selected men will have a mean weight that is greater than 175 lb. (Round to four decimal places as needed.) Please show all work as if...
An engineer is going to redesign an ejection seat for an airplane. The seat was designed...
An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and 171 lb. The new population of pilots has normally distributed weights with a mean of 138 lb and a standard deviation of 34.8 lb. a. If a pilot is randomly​ selected, find the probability that his weight is between 130 lb and 171 lb. The probability is approximately________. ​ (Round to four decimal places as​ needed.) b....