Question

an engineer is going to redesign an ejection seat for an airplane. the seat was designed for pilots weighing between 130lb and 171lb. The new population of pilots has normally distributed weights with a mean of 138lb and a standard deviation of 25.4lb.

An engine is going to redesignet for the seat was designed for poweging between 10 and 11 The new posts may distributed weights with a mean of 138 and a standard deviation of 24 la plata randomly selected in the probably that he is between 10 and 11 The probability is around to our compaces as needed

Answer 1

Solution :

Given that ,

mean = $\mu$ = 138

standard deviation = $\sigma$ = 25.4

P( 130 < x < 171)

= P[( 130 - 138) / 25.4) < (x - $\mu$ ) / $\sigma$   < ( 171 - 138) / 25.4) ]

= P( -0.31 < z < 1.30 )

= P(z < 1.30 ) - P(z < -0.31)

Using z table,

= 0.9032 - 0.3783

= 0.5249

The probability = 0.5249