An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 140 lb and 201 lb. The new population of pilots has normally distributed weights with a mean of 149 lb and a standard deviation of 32.2 lb.

A. If a pilot is randomly selected, find the probability that his weight is between 140 lb and 201 lb.

The probability is approximately:

B. If 35 different pilots are randomly selected, find the probability that their mean weight is between 140 lb and 201 lb.

The probability is approximately:

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.

answer for #1 is c

answer for #2 is d

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b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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