A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 183 lb and a standard deviation of 40 lb. The gondola has a stated capacity of 25 passengers, and the gondola is rated for a load limit of 3500 lb. Complete parts (a) through (d) below. a. Given that the gondola is rated for a load limit of 3500 lb, what is the maximum mean weight of the passengers i the gondola is filled to the stated capacity of 25 passengers? The maximum mean weight is 140 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 1.0000. (Round to four decimal places as needed.) c. If the weight assumptions were revised so that the new capacity became 20 passengers and the gondola is filled with 20 randomly selected skiers, what is the probability that their mean weight exceeds 175 lb, which is the maximum mean weight that does not cause the total load to exceed 3500 lb? The probability is .5000 (Round to four decimal places as needed.) d. Is the new capacity of 20 passengers safe? Since the probability of overloading is over 50%, the new capacity does not appear to be safe enough.
A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 183 lb and a standard deviation of 40 lb. The gondola has a stated capacity of 25 passengers, and the gondola is rated for a load limit of 3500 lb. Complete parts (a) through (d) below. a. Given that the gondola is rated for a load limit of 3500 lb, what is the maximum mean weight of the passengers i the gondola is filled to the stated capacity of 25 passengers? The maximum mean weight is 140 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 1.0000. (Round to four decimal places as needed.) c. If the weight assumptions were revised so that the new capacity became 20 passengers and the gondola is filled with 20 randomly selected skiers, what is the probability that their mean weight exceeds 175 lb, which is the maximum mean weight that does not cause the total load to exceed 3500 lb? The probability is .5000 (Round to four decimal places as needed.) d. Is the new capacity of 20 passengers safe? Since the probability of overloading is over 50%, the new capacity does not appear to be safe enough.
A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 183 lb and a standard deviation of 40 lb. The gondola has a stated capacity of 25 passengers, and the gondola is rated for a load limit of 3500 lb. Complete parts (a) through (d) below. a. Given that the gondola is rated for a load limit of 3500 lb, what is the maximum mean weight of the passengers i the gondola is filled to the stated capacity of 25 passengers? The maximum mean weight is 140 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 1.0000. (Round to four decimal places as needed.) c. If the weight assumptions were revised so that the new capacity became 20 passengers and the gondola is filled with 20 randomly selected skiers, what is the probability that their mean weight exceeds 175 lb, which is the maximum mean weight that does not cause the total load to exceed 3500 lb? The probability is .5000 (Round to four decimal places as needed.) d. Is the new capacity of 20 passengers safe? Since the probability of overloading is over 50%, the new capacity does not appear to be safe enough.
A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 183lb and a standard deviation of 40lb. The gondola has a stated capacity of 25 passengers, and the gondola is rated for a load limit of 3500lb. Complete parts (a) through (d) below.
Transcribed Image Text:A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a
mean of 183 lb and a standard deviation of 40 lb. The gondola has a stated capacity of 25 passengers, and the
gondola is rated for a load limit of 3500 lb. Complete parts (a) through (d) below.
a. Given that the gondola is rated for a load limit of 3500 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 140 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 1.0000
(Round to four decimal places as needed.)
c. If the weight assumptions were revised so that the new capacity became 20 passengers and the gondola is filled
with 20 randomly selected skiers, what is the probability that their mean weight exceeds 175 lb, which is the
maximum mean weight that does not cause the total load to exceed 3500 lb?
The probability is .5000
(Round to four decimal places as needed.)
d. Is the new capacity of 20 passengers safe?
Since the probability of overloading is over 50%, the new capacity does not appear to be safe enough.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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