Mathematics, 24.02.2020 22:33 dayjionneam

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)?

Answers: 2

Show answers

Answers

Answer from: slonekaitlyn01

(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.; $\mu$ = 160 lb and $\sigma$ = 27.5 lb

(A) We know that Z = $\frac{X - \mu}{\sigma}$ ~ 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( $\frac{X - \mu}{\sigma}$ < $\frac{201 - 155}{29.2}$ ) = P(Z < 1.57) = 0.94179

P(X <= 150) = P( $\frac{X - \mu}{\sigma}$ < $\frac{150 - 155}{29.2}$ ) = 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 = $\frac{Xbar - \mu}{\frac{\sigma}{\sqrt{n} } }$ ~ 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( $\frac{Xbar - \mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{201 - 155}{\frac{29.2}{\sqrt{39} } }$ ) = P(Z < 9.84) = 1 - P(Z >= 9.84)

= 0.999995

P(X bar <= 150) = P( $\frac{Xbar - \mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{150 - 155}{\frac{29.2}{\sqrt{39} } }$ ) = 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.

Answer from: Quest

child does not get an education so she can use the molla on junk

Answer from: Quest

see attached

step-by-step explanation:

given the function as;

$f(x)=2x^3-7x^2+2x+3$

write the equation replacing f(x) with y

$y=2x^3-7x^2+2x+3$

form and fill a table containing values of y with corresponding values of x

you can take a range for values of x as -3≤x≤3

solving for x=-3

$f(-3)=2*-3^3-7*-3^2+2*-3+3=2*-27-63+-6+3=-54-63-6+3y=-120$

for x=-2

$f(-2)=2*-2^3-7*-2^2+2*-2+3=2*-8-28+-4+3=-16-28-4+3=-45$

repeat the same procedure to get the values of y for the remaining ,x=-1 to x=3

plot the values of y against values of x and obtain the following graph

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 18:30, letsbestupidcx7734

Two cyclists 84 miles apart start riding toward each other at the samen time. one cycles 2 times as fast as the other. if they meet 4 hours later what is the speed (in miles) of the faster cyclists

Answers: 2

continue

Mathematics, 21.06.2019 20:30, icantspeakengles

In priyas math class there are 10 boys and 15 girls. what is the ratio of boys to girls in priyas math class? express your answer as a decimal

Answers: 1

continue

Mathematics, 21.06.2019 23:10, jaylenmiller437

Astudent draws two parabolas on graph paper. both parabolas cross the x-axis at (–4, 0) and (6, 0). the y-intercept of the first parabola is (0, –12). the y-intercept of the second parabola is (0, –24). what is the positive difference between the a values for the two functions that describe the parabolas? write your answer as a decimal rounded to the nearest tenth

Answers: 2

continue

Mathematics, 22.06.2019 00:00, vvaallww

Jonathan can throw a baseball 10 1/3 yards. his brother joey can throw a baseball 13 1/2 yards. how much father can joey throw the ball?

Answers: 1

continue

You know the right answer?

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots...