According to the June 2004 Readers' Digest article "Only in America," the average amount that a 17-year-old spends on his or her high school prom is $631 Assume that the amounts spent are normally distributed with a standard deviation of $166. (Give your answers correct to four decimal places.) (a) Find the probability that the mean cost to attend a high school prom for 30 randomly selected high school 17-year-olds is between $550 and $700. (b) Find the probability that the mean cost to attend a high school prom for 30 randomly selected high school 17-year-olds is greater than $759. (c) Do you think the assumption of normality is reasonable? Explain. Pick one...... If the normality assumption does not hold, then using the normal distribution is a reasonable approximate given that sample size n is ≥ 30. If the normality assumption does not hold, then using the normal distribution is not a reasonable approximate given that sample size n is ≥ 30. If the normality assumption does not hold, then using the normal distribution is a reasonable approximate given that sample size n is < 30. If the normality assumption does not hold, then using the normal distribution is not a reasonable approximate given that sample size n is < 30

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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According to the June 2004 Readers' Digest article "Only in America," the average amount that a 17-year-old spends on his or her high school prom is $631 Assume that the amounts spent are normally distributed with a standard deviation of $166. (Give your answers correct to four decimal places.)

(a) Find the probability that the mean cost to attend a high school prom for 30 randomly selected high school 17-year-olds is between $550 and $700.

(b) Find the probability that the mean cost to attend a high school prom for 30 randomly selected high school 17-year-olds is greater than $759.

(c) Do you think the assumption of normality is reasonable? Explain. Pick one......

If the normality assumption does not hold, then using the normal distribution is a reasonable approximate given that sample size n is ≥ 30.

If the normality assumption does not hold, then using the normal distribution is not a reasonable approximate given that sample size n is ≥ 30.

If the normality assumption does not hold, then using the normal distribution is a reasonable approximate given that sample size n is < 30.

If the normality assumption does not hold, then using the normal distribution is not a reasonable approximate given that sample size n is < 30.

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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