Why a large sample is needed for the distribution of the sample proportion to be approximately normal.

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Answer 1

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Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 8, Problem 6CT

a.

To determine

To explain: Why a large sample is needed for the distribution of the sample proportion to be approximately normal.

b.

To determine

Whether it is unusual if a random sample of 1,500 Americans results in fewer than 10 with peanut or tree nut allergies.

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An environmental research team is studying the daily rainfall (in millimeters) in a region over 100 days. The data is grouped into the following histogram bins: Rainfall Range (mm) Frequency 0-9.9 15 10 19.9 25 20-29.9 30 30-39.9 20 ||40-49.9 10 a) If a random day is selected, what is the probability that the rainfall was at least 20 mm but less than 40 mm? b) Estimate the mean daily rainfall, assuming the rainfall in each bin is uniformly distributed and the midpoint of each bin represents the average rainfall for that range. c) Construct the cumulative frequency distribution and determine the rainfall level below which 75% of the days fall. d) Calculate the estimated variance and standard deviation of the daily rainfall based on the histogram data.

An electronics company manufactures batches of n circuit boards. Before a batch is approved for shipment, m boards are randomly selected from the batch and tested. The batch is rejected if more than d boards in the sample are found to be faulty. a) A batch actually contains six faulty circuit boards. Find the probability that the batch is rejected when n = 20, m = 5, and d = 1. b) A batch actually contains nine faulty circuit boards. Find the probability that the batch is rejected when n = 30, m = 10, and d = 1.

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Answer 2

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Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 8, Problem 6CT

a.

To determine

To explain: Why a large sample is needed for the distribution of the sample proportion to be approximately normal.

b.

To determine

Whether it is unusual if a random sample of 1,500 Americans results in fewer than 10 with peanut or tree nut allergies.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 8, Problem 6CT

a.

To determine

To explain: Why a large sample is needed for the distribution of the sample proportion to be approximately normal.

b.

To determine

Whether it is unusual if a random sample of 1,500 Americans results in fewer than 10 with peanut or tree nut allergies.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 8, Problem 6CT

a.

To determine

To explain: Why a large sample is needed for the distribution of the sample proportion to be approximately normal.

b.

To determine

Whether it is unusual if a random sample of 1,500 Americans results in fewer than 10 with peanut or tree nut allergies.

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Answer 5

Chapter 8, Problem 6CT

a.

To determine

To explain: Why a large sample is needed for the distribution of the sample proportion to be approximately normal.

b.

To determine

Whether it is unusual if a random sample of 1,500 Americans results in fewer than 10 with peanut or tree nut allergies.

Answer 6

Chapter 8, Problem 6CT

a.

To determine

To explain: Why a large sample is needed for the distribution of the sample proportion to be approximately normal.

Answer 7

Chapter 8, Problem 6CT

a.

To determine

To explain: Why a large sample is needed for the distribution of the sample proportion to be approximately normal.

Answer 8

b.

To determine

Whether it is unusual if a random sample of 1,500 Americans results in fewer than 10 with peanut or tree nut allergies.

Answer 9

b.

To determine

Whether it is unusual if a random sample of 1,500 Americans results in fewer than 10 with peanut or tree nut allergies.

Answer 10

Expert Solution & Answer

Answer 11

Expert Solution & Answer

Answer 12

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Answer 13

Ch. 8.1 - The _____ _____ of the sample mean, x, is the...Ch. 8.1 - Suppose a simple random sample of size n is drawn...Ch. 8.1 - The standard deviation of the sampling...Ch. 8.1 - True or False: The distribution of the sample...Ch. 8.1 - True or False: The distribution of the sample...Ch. 8.1 - True or False: To cut the standard error of the...Ch. 8.1 - A simple random sample of size n = 10 is obtained...Ch. 8.1 - A simple random sample of size n = 40 is obtained...Ch. 8.1 - In Problems 912, determine x and x from the given...Ch. 8.1 - In Problems 912, determine x and x from the given...

Why a large sample is needed for the distribution of the sample proportion to be approximately normal.

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Whether it is unusual if a random sample of 1,500 Americans results in fewer than 10 with peanut or tree nut allergies.

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