![gibesanna11p5nn28](/avatars/23125.jpg)
gibesanna11p5nn28
24.02.2020 •
Mathematics
An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 150 lb and 191 lb. The new population of pilots has normally distributed weights with a mean of 155 lb and a standard deviation of 29.2 lb.
(a) If a pilot is randomly selected, find the probability that his weight is between 150 lb and 201 lb.
(b) If 39 different pilots are randomly selected, find the probability that their mean weight is between 150 lb and 201 lb.
(c) When redesigning the ejection seat which probability is more relevant
Part (a) or Part (b)?
Solved
Show answers
More tips
- C Computers and Internet Step-by-Step Guide on How to Download Music to Your iPhone...
- A Animals and plants Unraveling the Mystery of Loch Ness: What Does the Loch Ness Monster Look Like?...
- L Leisure and Entertainment Should You Buy a Ceramic Knife?...
- C Computers and Internet How to easily and quickly disable Firebug in Gmail and Google Docs...
- G Goods and services How to sew a ribbon: Tips for beginners...
- F Food and Cooking How to Make Mayonnaise at Home? Secrets of Homemade Mayonnaise...
- C Computers and Internet Which Phone is Best for Internet Surfing?...
- F Food and Cooking Everything You Need to Know About Pasta...
- C Computers and Internet How to Choose a Monitor?...
- H Horoscopes, Magic, Divination Where Did Tarot Cards Come From?...
Answers on questions: Mathematics
- M Mathematics Edgardo has a drink cooler that holds 10 gallons of water. He is filling the cooler with a 1−quart container. gal 1 2 3 4 10 qt 4 8 12 16 40 What if Edgardo only uses 24...
- M Mathematics I need help on algebra...
- M Mathematics Helppp me plz im begging u...
- M Mathematics Suppose that A is 3 x 3 matrix. Suppose the following sequence of elementary row operations, labeled E1, E2, and E3, turn A into the identity matrix I3. E1: Rows one and...
- M Mathematics Determine the number of observations that would be required to estimate the mean time for the first element within 4 percent of the true value with a confidence of 98 percent....
- M Mathematics Can someone help me! Solve for g thank you....
- M Mathematics A 15 foot pole extends & feet below ground and 10 feet above ground. Choose the linear equation that models the situation....
- M Mathematics The value that satisfies the equation 7/n=8/7 is...
- M Mathematics State the domain and range of the following function. {(6,-8), (9,3), (-3,5), (1,-6), (5,7)}...
- M Mathematics Subtract b (b2 +b -7) + 5 from 3b2 – 8 and find the value of expression obtained for b = -3....
Ответ:
(a) 0.50928
(b) 0.857685.
Step-by-step explanation:
We are given that an engineer is going to redesign an ejection seat for an airplane. The new population of pilots has normally distributed weights with a mean of 155 lb and a standard deviation of 29.2 lb i.e.;
= 160 lb and
= 27.5 lb
(A) We know that Z =
~ N(0,1)
Let X = randomly selected pilot
If a pilot is randomly selected, the probability that his weight is between 150 lb and 201 lb = P(150 < X < 201)
P(150 < X < 201) = P(X < 201) - P(X <= 150)
P(X < 201) = P(
<
) = P(Z < 1.57) = 0.94179
P(X <= 150) = P(
<
) = P(Z < -0.17) = 1 - P(Z < 0.17) = 1 - 0.56749
= 0.43251
Therefore, P(150 < X < 201) = 0.94179 - 0.43251 = 0.50928 .
(B) We know that for sampling mean distribution;
Z =
~ N(0,1)
If 39 different pilots are randomly selected, the probability that their mean weight is between 150 lb and 201 lb is given by P(150 < X bar < 210);
P(150 < X bar < 210) = P(X bar < 201) - P(X bar <= 150)
P(X bar < 201) = P(
<
) = P(Z < 9.84) = 1 - P(Z >= 9.84)
= 0.999995
P(X bar <= 150) = P(
<
) = P(Z < -1.07) = 1 - P(Z < 1.07)
= 1 - 0.85769 = 0.14231
Therefore, P(150 < X bar < 210) = 0.999995 - 0.14231 = 0.857685.
C) If the tolerance level is very high to accommodate an individual pilot then it should be appropriate ton consider the large sample i.e. Part B probability is more relevant in that case.
Ответ: