A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 202 lb and a standard deviation of 43 lb. The gondola has a stated capacity of 25 ​passengers, and the gondola is rated for a load limit of 3750 lb. Complete parts​ (a) through​ (c) below.   a. Given that the gondola is rated for a load limit of 3750​lb, what is the maximum mean weight of the passengers if the gondola is filled to the stated capacity of 25 ​passengers? The maximum mean weight is ______ lb. ​(Type an integer or a decimal. Do not​ round.)   b. If the gondola is filled with 25 randomly selected​ skiers, what is the probability that their mean weight exceeds the value from part​ (a)?The probability is _______ (Round to four decimal places as​ needed.)   c. If the weight assumptions were revised so that the new capacity became 20passengers and the gondola is filled with 20 randomly selected​ skiers, what is the probability that their mean weight exceeds 187.5 ​lb, which is the maximum mean weight that does not cause the total load to exceed 3750 ​lb? The probability is ________ ​(Round to four decimal places as​ needed.)

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A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 202 lb and a standard deviation of 43 lb. The gondola has a stated capacity of 25 ​passengers, and the gondola is rated for a load limit of 3750 lb. Complete parts​ (a) through​ (c) below.

 

a. Given that the gondola is rated for a load limit of
3750​lb, what is the maximum mean weight of the passengers if the gondola is filled to the stated capacity of 25 ​passengers? The maximum mean weight is ______ lb. ​(Type an integer or a decimal. Do not​ round.)
 
b. If the gondola is filled with 25 randomly selected​ skiers, what is the probability that their mean weight exceeds the value from part​ (a)?The probability is _______ (Round to four decimal places as​ needed.)
 
c. If the weight assumptions were revised so that the new capacity became
20passengers and the gondola is filled with 20 randomly selected​ skiers, what is the probability that their mean weight exceeds 187.5
​lb, which is the maximum mean weight that does not cause the total load to exceed 3750 ​lb? The probability is ________ ​(Round to four decimal places as​ needed.)
 
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