The capacity of an elevator is 12 people or 1908 pounds. The capacity will be ex
ID: 3230379 • Letter: T
Question
The capacity of an elevator is 12 people or 1908 pounds. The capacity will be exceeded if 12 people have weights with a mean greater than 1908/12=159 pounds. Suppose the people have weights that are normally distributed with a mean of 162 pounds and a standard deviation of 31 pounds.A) The probability that if a person is randomly selected, his weight will be greater than 159 pounds.
B) find the probability that the mean of 12 randomly selected people will have a mean that is greater than 159 pounds. The capacity of an elevator is 12 people or 1908 pounds. The capacity will be exceeded if 12 people have weights with a mean greater than 1908/12=159 pounds. Suppose the people have weights that are normally distributed with a mean of 162 pounds and a standard deviation of 31 pounds.
A) The probability that if a person is randomly selected, his weight will be greater than 159 pounds.
B) find the probability that the mean of 12 randomly selected people will have a mean that is greater than 159 pounds.
A) The probability that if a person is randomly selected, his weight will be greater than 159 pounds.
B) find the probability that the mean of 12 randomly selected people will have a mean that is greater than 159 pounds.
Explanation / Answer
Mean is 162 and sd is 31
a) P(x>159)=P(z>(159-162)/31)=P(z>-0.096) or 1-P(z<0.1) from normal table it is 0.5398
b) for 12 people standard error is 31/sqrt(12)=8.95
or P(xbar>159)=P(z>(159-162)/8.95)=P(z>-0.3352) or P(z<0.34) from normal table is 0.6331
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