I need original answers ( Tyed up ) for bot hquestiosn please An engineer is goi

Question

I need original answers ( Tyed up ) for bot hquestiosn please

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 120 lb and 171 lb. The new population of pilots has normally distributed weights with a mean of 127 lb and a standard deviation of 30.5 lb.

a. If a pilot is randomly selected, find the probability that his weight is between 120lb and 171 lb

The probability is approximately:              Round to four decimal places as needed.

2) If np greater than or equals 5 and np5 , estimate P(fewer than 4) with n= 14 and p=0.5 by using the normal distribution as an approximation to the binomial distribution; if np <5 or np<5, then state that the normal approximation is not suitable

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

A: P(fewer than 4) =                              (Round to four decimal places as needed)

B: The normal approximation is not suitable

Explanation / Answer

1) Given

Mean = 127 , Standard deviation =30.5

(a) The probability that his weight is between 120 lb and 171 lb is

P( 120 < x <171 ) is

if x = 120 then Z = (x - mean) / ( standard deviation)

Z = ( 120 - 127 ) / (30.5)

Z = -7 / 30.5 = - 0.2295

z - score = - 0.23

if x = 171 then Z = ( 171 - 127 ) / (30.5)

Z = 1.4426

Z - score = 1.44

P( 120 < x <171 ) = P( - 0.23 < z < 1.44)

= P(Z < 1.44) - P(Z < - 0.23)

= 0.9251 - 0.4090 = 0.5161

P( 120 < x <171 ) = 0.5161

2) Given n = 14, p = 0.5

So, np = 7

np5 so estimate P(fewer than 4)

P(fewer than 4) is

If P ( x < 4) =

you should use correction factor for continuty, So

P ( x < 4) = P ( x < 3.5) =

Then Z = (x - np) / sqrt(npq)   

Z = 3.5 - 7/ sqrt(3.5) = - 1.870829 ~ - 1.87

P(Z < - 1.87) = 0.0307

P ( x < 4) = 0.0307

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