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Ganezh [65]
3 years ago
12

An engineer is going to redesign an ejection seat for an airplane. the seat was designed for pilots weighing between 130lb and 1

71lb. The new population of pilots has normally distributed weights with a mean of 137lb and a standard deviation of 28.9lb. If a pilot is randomly selected find the probability that his weight is between 130lb and 171lb​
Mathematics
1 answer:
Vlad [161]3 years ago
6 0

Answer: 0.4758

Step-by-step explanation:

Given : Mean : \mu=137\text{ lb}

Standard deviation : \sigma =28.9\text{ lb}

Also, the new population of pilots has normally distributed .

The formula to calculate the z-score :-

z=\dfrac{x-\mu}{\sigma}

For x=130 lb .

z=\dfrac{130-137}{28.9}=-0.2422145\approx-0.24

For x=171lb.

z=\dfrac{171-137}{28.9}=1.1764705\approx1.18

The p-value =P(-0.24

=0.8809999-0.4051651=0.4758348\approx0.4758348\approx0.4758

Hence, the required probability : 0.4758

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Calculate an estimate for the mean temperature
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The temperature was in the range of 10-13 on 7 of the days.
Give it the weight of the middle of the range = 11.5 for 7 times = 80.5

The temperature was in the range of 14-17 on 9 of the days.
Give it the weight of the middle of the range = 15.5 for 9 times = 139.5

The temperature was in the range of 18-21 on 16 of the days.
Give it the weight of the middle of the range = 19.5 for 16 times = 312

The temperature was in the range of 22-25 on 22 of the days.
Give it the weight of the middle of the range = 23.5 for 22 times = 517

The temperature was in the range of 26-29 on 6 of the days.
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