Probability Questions

1) An engineer is going to redesign an ejection seat for an airplane. The seat was designed by pilots weighing between 150 lb and 191 lb. The new population of pilots has normally distributed weights with a mean of 157 lb and a standard deviation of 32.3 lb.

a) if a pilot is randomly selected, find the probability that his weight is between 150 lb and 191 lb.

please show all work as I need to understand

2) If np>5 and nq>5, estimate P (fewer than 3) with n =14 and p=0.4 by using the normal distribution as an approximation of the binomial distribution, if np<5 or nq<5, then state that the normal approximation is not suitable.

a) P(fewer than 3) = ________________ (round to four decimals)

b) the normal approximateion is not suitable?

please show all work as I need to understand

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