An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 140 lb and 181 lb. The new population of pilots has normally distributed weights with a mean of 146 lb and a standard deviation of 33.4 lb. a. If a pilot is randomly selected, find the probability that his weight is between 140 lb and 181 lb. The probability is approximately 0.4245. (Round to four decimal places as needed.) b. If 32 different pilots are randomly selected, find the probability that their mean weight is between 140 lb and 181 Ib. HERS The probability is approximately (Round to four decimal places as needed.) 30 dliferent pilots are randomly selected, find the probability that their mean weight is between 140 lb and 191 lb. The probability is approximately (Round to four decimal places as needed.) c. When redesigning the ejection seat, which probability is more relevant? O A. Part (a) because the seat performance for a single pilot is more important. O B. Part (b) because the seat performance for a sample of pilots is more important. OC. Part (a) because the seat performance for a sample of pilots is more important. O D. Part (b) because the seat performance for a single pilot is more important. Show transcribed image text
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Can you assist me in answering questions b and c, please?
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