The distribution of actual weights of wedges of cheddar cheese produced at a dairy is normal with a mean of 8.8 ounces and a standard deviation of 0.2 ounces. (Round to 2decimal places for all z-values and round all other answers to 4 decimal places, if needed.)(a) The probability that a randomly chosen wedge of cheddar cheese is greater than 8.75 is(b) If a sample of 17 is randomly chosen, then the distribution of the sample mean weight is approximately normal with.deviation of(c) The probability that the sample mean weight of this sample of 17 is less than 8.75 is(d) The probability that the sample mean weight of this sample of 17 is greater than 8.75 is(e) The probability that the sample mean weight of this sample of 17 is between 8.75 and 8.86 is(f) There is only a 4% chance that the average weight of a sample of these 17 cheese wedges will be belowCheckmean ofand a standard

Let X be the random variable for the actual weight of cheddar cheese at a dairy. Given that, X ~…

Answered: (a) The probability that a randomly…

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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52) The overhead reach distances of adult females are normally distributed with a mean of 200 cm and a standard deviation of 8.6 cm. a. Find the probability that an individual distance is greater than 209.30 cm. b. Find the probability that the mean for 20 randomly selected distances is greater than 198.20 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
The distribution of age of a certain professional sport is strongly skewed to the right with mean 26.8 years and standard deviation 4.2. Consider a random sample of 4 players and a different random sample of 50 players from the population. Which of the following statements is true about the sampling distributions of the sample mean ages for samples of size 4 and samples of size 50
Suppose that you have a large number of potatoes. The mean weight of the potatoes is 7.4 ounces with a standard deviation of 2.2 ounces. We may assume a normal distribution. c) If you choose 40 potatoes at random, what is the probability that the mean of this sample of 40 potatoes is more than 7.5 ounces?
A study by the American Heart Association studied the distribution of birth weights for 1295 newborns (preterm babies excluded). They found that the birth weight of human babies is approximately normally distributed with a mean of 7.6 pounds and a standard deviation of 1.09 pounds. (a.) What is the probability that a randomly chosen baby weighs more than 9 pounds at birth? (b.) What is the probability that a randomly chosen baby weights between 6 and 8 pounds at birth? (c.) What is the 80th percentile for birth weight?
The average fuel efficiency of U.S. light vehicles (cars, SUVs, minivans, vans, and light trucks) for 2005 was 21 miles per gallon (mpg). If the standard deviation of the population was 2.8 and the gas ratings were normally distributed, (a) what is the probability that the mean mpg for a random sample of 25 light vehicles is under 18? (b) between 20 and 24?
The height of American women is believed to follow a normal distribution with mean μ = 5.38 feet and standard deviation σ = 0.2083 feet. (b) A study randomly selects 30 American women. What is the probability that the mean height of women in this sample is greater than 5.5 feet? (c) Another study randomly selects 50 American women. Will there be a lower or higher probability that the mean height of the 50 women in this sample is greater than 5.5 feet, compared to the study in part (b)? Explain. (d) Instead, for which of the two studies from parts (b) and (c) there is a higher probability that the mean height of the women in the sample is between 5.33 and 5.43 feet? Explain.
Suppose that 70% of residents in a certain city own at least one pet. You select a random sample of 30 city residents. Let X = the number of residents that own at least one pet. Would it be appropriate to use a normal distribution to model the sampling distribution of X? No, there are at least 10 "successes" expected, but there are not at least 10 "failures" expected. It is not appropriate to use a normal distribution to model the sampling distribution of X. No, the sample size is greater than 10, so it is not appropriate to use a normal distribution to model the sampling distribution of X. Yes, the sample size is at least 30, so it is appropriate to use a normal dist bution to model the sampling distr ution of X. Yes, there are at least 10 "successes" expected and 10 "failures" expected so it is appropriate to use a normal distribution to model the sampling distribution of X. No, there are not at least 10 "successes" expected, although there are at least 10 "failures" expected. It is…
A company produces boxes of cereals with a standard deviation of 10 grams. The population distribution of weights is the normal distribution. According to this:1. If 9 boxes are selected randomly from the production line, what is the probability that the sample mean is at least 5 grams higher than the population average?2. What should be the sample size so that the difference between the sample mean and the population mean (two-way) is less than 0.01 grams?
In the field of accountancy, times spent studying by students in the week before professional exams follow a Normal distribution with a standard deviation of 8 hours. A random sample of 4 students was taken in order to estimate the mean study time for the population of all students. a) What is the probability that the sample mean exceeds the population mean by more than 2 hours? b) What is the probability that the sample mean differs from the population mean by more than 4 hours? c) Suppose that a second (independent) random sample of 10 students was taken. Without doing any calculations, state whether the probabilities in parts (a) and (b) would be higher, lower or the same for the second sample.
The height of women ages 20-29 is normally distributed, with a mean of 63.7 inches. Assume σ=2.3 inches. What is the probability of randomly selecting 1 woman with a height less than 65.2 inches? (Round to four decimal places as needed.) What is the probability of selecting a sample of 23 women with a mean height less than 65.2 inches?
7
An automobile insurer has found that repair claims are Normally distributed with a mean of $510 and a standard deviation of $460. (a) Find the probability that a single claim, chosen at random, will be less than $480.ANSWER: (b) Now suppose that the next 50 claims can be regarded as a random sample from the long-run claims process. Find the probability that the average x¯of the 50 claims is smaller than $480.ANSWER:

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