Question Help ween 150 Ib and 201 Ib An engineer is going to redesign an ejectio

Question

Question Help ween 150 Ib and 201 Ib An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing be The new population of pilots has normally distributed weights with a mean of 157 lb and a standard deviation of 299 Ib a. If a pilot is randomly selected, find the probability that his weight is between 150 Ib and 201 lb The probability is approximately (Round to four decimal places as needed) 1 different pilots are randomly selected, find the probability that their mean weight is between 150 lb and 201 lb. The probability is approximately [ (Round to four decimal places as needed ) c. When redesigning the ejection seat, which probability is more relevant? O A. Part (a) because the seat performance for a single pilot is more important Part (b) because the seat performance for a single pilot is more important Part (a) because the seat performance for a sample of pilots is more important Part (b) because the seat performance for a sample of pilots is more important. B. ° C. D.

Explanation / Answer

Solution:

mean = 157
sd = 29.9
a) z = (150-157)/29.9 = -0.234
z = (201-157)/29.9 =1.472
Want z-values between these two numbers. It is 0.5202
b) This increases the z-value by a factor of the sqrt(31) = 5.568
(x-mean)/[sd/sqrt(31)] ; Dividing, we invert, so all the above values are multiplied by 5.5677
z = (150-157)/[29.9/sqrt(31)] = -1.3035
z = (201-157)/[29.9/sqrt(31)] = 8.1933

probability is between these two values, which is almost 1.
Actual is 0.9032

c)When redesigning the ejection seat, the probability of the mean weight of the pilots is relevant, as its probability is more as compares to that of individual weight
i.e., 0.5202< 0.9032
Therefore, the correct option is D

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.