You may need to use the appropriate appendix table or technology to answer this question. The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 4 inches. A sample of 33 years of rainfall for California and a sample of 46 years of rainfall for New York has been taken. (a) Show the probability distribution of the sample mean annual rainfall for California. A bell-shaped curve is above a horizontal axis labeled inches. The horizontal axis ranges from about 10 to about 34. The curve enters the viewing window near 10 just above the horizontal axis, curves up to the right, and reaches a maximum near 22. The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 34. A bell-shaped curve is above a horizontal axis labeled inches. The horizontal axis ranges from about 39.9 to about 44.1. The curve enters the viewing window near 39.9 just above the horizontal axis, curves up to the right, and reaches a maximum near 42. The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 44.1. A bell-shaped curve is above a horizontal axis labeled inches. The horizontal axis ranges from about 19.9 to about 24.1. The curve enters the viewing window near 19.9 just above the horizontal axis, curves up to the right, and reaches a maximum near 22. The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 24.1. A bell-shaped curve is above a horizontal axis labeled inches. The horizontal axis ranges from about −2.1 to about 2.1. The curve enters the viewing window near −2.1 just above the horizontal axis, curves up to the right, and reaches a maximum near 0. The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 2.1. (b) What is the probability that the sample mean is within 1 inch of the population mean for California? (Round your answer to four decimal places.) (c) What is the probability that the sample mean is within 1 inch of the population mean for New York? (Round your answer to four decimal places.)

You may need to use the appropriate appendix table or technology to answer this question. The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 4 inches. A sample of 33 years of rainfall for California and a sample of 46 years of rainfall for New York has been taken. (a) Show the probability distribution of the sample mean annual rainfall for California. A bell-shaped curve is above a horizontal axis labeled inches. The horizontal axis ranges from about 10 to about 34. The curve enters the viewing window near 10 just above the horizontal axis, curves up to the right, and reaches a maximum near 22. The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 34. A bell-shaped curve is above a horizontal axis labeled inches. The horizontal axis ranges from about 39.9 to about 44.1. The curve enters the viewing window near 39.9 just above the horizontal axis, curves up to the right, and reaches a maximum near 42. The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 44.1. A bell-shaped curve is above a horizontal axis labeled inches. The horizontal axis ranges from about 19.9 to about 24.1. The curve enters the viewing window near 19.9 just above the horizontal axis, curves up to the right, and reaches a maximum near 22. The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 24.1. A bell-shaped curve is above a horizontal axis labeled inches. The horizontal axis ranges from about −2.1 to about 2.1. The curve enters the viewing window near −2.1 just above the horizontal axis, curves up to the right, and reaches a maximum near 0. The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 2.1. (b) What is the probability that the sample mean is within 1 inch of the population mean for California? (Round your answer to four decimal places.) (c) What is the probability that the sample mean is within 1 inch of the population mean for New York? (Round your answer to four decimal places.)

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.7: Probability

Problem 1SE: What term is used to express the likelihood of an event occurring? Are there restrictions on its...

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QUESTION 7

You may need to use the appropriate appendix table or technology to answer this question.

The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 4 inches. A sample of 33 years of rainfall for California and a sample of 46 years of rainfall for New York has been taken.

(a)

Show the probability distribution of the sample mean annual rainfall for California.

A bell-shaped curve is above a horizontal axis labeled inches.

The horizontal axis ranges from about 10 to about 34.
The curve enters the viewing window near 10 just above the horizontal axis, curves up to the right, and reaches a maximum near 22.
The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 34.

A bell-shaped curve is above a horizontal axis labeled inches.

The horizontal axis ranges from about 39.9 to about 44.1.
The curve enters the viewing window near 39.9 just above the horizontal axis, curves up to the right, and reaches a maximum near 42.
The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 44.1.

A bell-shaped curve is above a horizontal axis labeled inches.

The horizontal axis ranges from about 19.9 to about 24.1.
The curve enters the viewing window near 19.9 just above the horizontal axis, curves up to the right, and reaches a maximum near 22.
The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 24.1.

A bell-shaped curve is above a horizontal axis labeled inches.

The horizontal axis ranges from about −2.1 to about 2.1.
The curve enters the viewing window near −2.1 just above the horizontal axis, curves up to the right, and reaches a maximum near 0.
The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 2.1.

(b)

What is the probability that the sample mean is within 1 inch of the population mean for California? (Round your answer to four decimal places.)

(c)

What is the probability that the sample mean is within 1 inch of the population mean for New York? (Round your answer to four decimal places.)

(d)

In which case, part (b) or part (c), is the probability of obtaining a sample mean within 1 inch of the population mean greater? Why?

part (c), because the population standard deviation is smallerpart (c), because the sample size is larger part (b), because the population standard deviation is smallerpart (b), because the standard error is smaller

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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