6. Awater taxi carries passengers from harbor to another. Assume that weights of passengers are normally distributed with a mean of 196 Ib and a standard deviation of 42 lb. The water tax has a stated capacity of 25 passengers, and the water taxi was rated for a load limit of 3750 Ib. Complete parts (a) through (d) below. a. Given that the water taxi was rated for a load limit of 3750 lb, what is the maximum mean weight of the passengers if the water taxi is filled to the stated capacity of 25 passengers? Ib. (Type an integer or a decimal. Do not round.) The maximum mean weight is b. If the water taxi is filled with 25 randomly selected passengers, 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 20 passengers and the water taxi is filled with 20 randomly selected passengers, 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.) d. Is the new capacity of 20 passengers safe? Since the probability of overloading is (1). the new capacity (2) to be safe enough.
6. Awater taxi carries passengers from harbor to another. Assume that weights of passengers are normally distributed with a mean of 196 Ib and a standard deviation of 42 lb. The water tax has a stated capacity of 25 passengers, and the water taxi was rated for a load limit of 3750 Ib. Complete parts (a) through (d) below. a. Given that the water taxi was rated for a load limit of 3750 lb, what is the maximum mean weight of the passengers if the water taxi is filled to the stated capacity of 25 passengers? Ib. (Type an integer or a decimal. Do not round.) The maximum mean weight is b. If the water taxi is filled with 25 randomly selected passengers, 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 20 passengers and the water taxi is filled with 20 randomly selected passengers, 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.) d. Is the new capacity of 20 passengers safe? Since the probability of overloading is (1). the new capacity (2) to be safe enough.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:6. A water taxi carries passengers from harbor to another. Assume that weights of passengers
are normally distributed with a mean of 196 Ib and a standard deviation of 42 lb. The water taxi
has a stated capacity of 25 passengers, and the water taxi was rated for a load limit of 3750
Ib. Complete parts (a) through (d) below.
a. Given that the water taxi was rated for a load limit of 3750 Ib, what is the maximum mean
weight of the passengers if the water taxi is filled to the stated capacity of 25 passengers?
The maximum mean weight is
Ib.
(Type an integer or a decimal. Do not round.)
b. If the water taxi is filled with 25 randomly selected passengers, 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 20 passengers
and the water taxi is filled with 20 randomly selected passengers, 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 Ib?
The probability is
(Round to four decimal places as needed.)
d. Is the new capacity of 20 passengers safe?
Since the probability of overloading is (1)
the new capacity
(2).
to be safe enough.
(1) O over 50%,
O under 5%,
(2)
appears
O does not appear
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