A boat capsized and sank in a lake. Based on an assumption of a mean weight of 138 lb, the boat was rated to carry 70 passengers (so the load limit was 9,660 lb). After the boat sank, the assumed mean weight for similar boats was changed from 138 lb to 172 lb. Complete parts a and b below. 3 Part Question... Part 1 A. Assume that a similar boat is loaded with 70 passengers, and assume that the weights of people are normally distributed with a mean of 178.1 lb and a standard deviation of 37.9 lb. Find the probability that the boat is overloaded because the 70 passengers have a mean weight greater than 138 lb. The probability is (Blank). (Round to four decimal places as needed.) Part 2 B. The boat was later rated to carry only 16 passengers, and the load limit was changed to 2,752 lb. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 172 (so that their total weight is greater than the maximum capacity of 2,752 lb). The probability is (Blank). (Round to four decimal places as needed.) Part 3 C. Do the new ratings appear to be safe when the boat is loaded with 16 passengers? Choose the correct answer below. A. Because 178.1 is greater than 172, the new ratings do not appear to be safe when the boat is loaded with 16 passengers. B. Because there is a high probability of overloading, the new ratings do not appear to be safe when the boat is loaded with 16 passengers. C. Because there is a high probability of overloading, the new ratings appear to be safe when the boat is loaded with 16 passengers. D. Because the probability of overloading is lower with the new ratings than with the old ratings, the new ratings appear to be safe.

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Description: A boat capsized and sank in a lake. Based on an assumption of a mean weight of 138 lb, the boat was rated to carry 70 passengers (so the load limit was 9,660 lb). After the boat sank, the assumed mean weight for similar boats was changed from 138

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 13PPS

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A boat capsized and sank in a lake. Based on an assumption of a mean weight of 138 lb, the boat was rated to carry 70 passengers (so the load limit was 9,660 lb). After the boat sank, the assumed mean weight for similar boats was changed from 138 lb to 172 lb. Complete parts a and b below.

3 Part Question...

Part 1

A. Assume that a similar boat is loaded with 70 passengers, and assume that the weights of people are normally distributed with a mean of 178.1 lb and a standard deviation of 37.9 lb. Find the probability that the boat is overloaded because the 70 passengers have a mean weight greater than 138 lb.

The probability is (Blank). (Round to four decimal places as needed.)

Part 2

B. The boat was later rated to carry only 16 passengers, and the load limit was changed to 2,752 lb. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 172 (so that their total weight is greater than the maximum capacity of 2,752 lb).

The probability is (Blank).

(Round to four decimal places as needed.)

Part 3

C. Do the new ratings appear to be safe when the boat is loaded with 16 passengers? Choose the correct answer below.

A. Because 178.1 is greater than 172, the new ratings do not appear to be safe when the boat is loaded with 16 passengers.

B. Because there is a high probability of overloading, the new ratings do not appear to be safe when the boat is loaded with 16 passengers.

C. Because there is a high probability of overloading, the new ratings appear to be safe when the boat is loaded with 16 passengers.

D. Because the probability of overloading is lower with the new ratings than with the old ratings, the new ratings appear to be safe.

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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