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Answer :
Final answer:
The probability that a randomly selected pilot's weight is between 140lb and 201lb is approximately 0.6284, calculated using the conversion to z-scores and the standard normal distribution.
Explanation:
In this question of probability, we are given that the weights of the new population of pilots are normally distributed with a mean of 145lb and a standard deviation of 29.7lb. We are asked to find the probability that a randomly selected pilot weighs between 140lb and 201lb.
To solve this, we first convert the weights into z-scores (a z-score gives us an idea of how far from the mean a data point is). For 140lb and 201lb, the z-scores can be calculated as follows: Z = (X - μ) / σ, where X is the weight, μ is the mean weight and σ is the standard deviation. This gives us z1 = (140 - 145) / 29.7 = -0.1683 and z2 = (201 - 145) / 29.7 = 1.8855.
The probability that a randomly selected pilot's weight is between 140lb and 201lb is the area under the standard normal curve between these z-scores, which can be found in the standard normal distribution table or calculated with a statistical program. The required probability is approximately 0.6284 (rounded to four decimal places).
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