(a) Explanation Calculation: Conditions for normal approximation to the binomial: For a binomial experiment with n number of trails, r number of success, probability of success for each trail p and probability of failure q = 1 − p , the r has binomial distribution which is approximated to a normal distribution if, n p > 5 n q > 5 Mean: The mean formula for the binomial distribution using normal approximation is, μ = n p In the formula n denotes number of trails, and p denotes probability of success. Standard deviation: The standard deviation formula for the binomial distribution using normal approximation is, σ = n p q In the formula q = 1 − p , n denotes number of trails, and p denotes probability of success. Conditions for Continuity correction: The continuity correction is used for converting the discrete random variable r denoting the number of success to continuous normal random variable x , The value x is obtained by subtracting 0.5 from r when r is the left point for an interval. That is, x = r − 0.5 . The value x is obtained by adding 0.5 from r when r is the right point for an interval. That is, x = r + 0.5 . Z score: The number of standard deviations the original measurement x is from the value of mean μ is measured using the z -score or z value. The formula for z score is, z = x − μ σ In the formula, x is the raw score, μ is the mean and σ is the standard deviation. Let r denotes the number of new products introduced in grocery stores fail (are taken off the market) within 2 years. A grocery store chain introduces 66 new products. That is, n = 66 , and the probability of success for each trail is p = 0.80 . Checking conditions: n p = 66 ( 0.80 ) = 52.8 > 5 n q = n ( 1 − p ) = 66 ( 1 − 0 (b) To determine Find the probability that within 2 years 58 or fewer fail. (c) To determine Find the probability that within 2 years 15 or more succeed. (d) To determine Find the probability that within 2 years fewer than 10 succeed.

Understandable Statistics: Concepts and Methods

12th Edition

ISBN: 9781337119917

Author: Charles Henry Brase, Corrinne Pellillo Brase

Publisher: Cengage Learning

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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 6.6, Problem 11P

(a)

To determine

Find the probability that within 2 years 47 or more fail.

(b)

To determine

Find the probability that within 2 years 58 or fewer fail.

(c)

To determine

Find the probability that within 2 years 15 or more succeed.

(d)

To determine

Find the probability that within 2 years fewer than 10 succeed.

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Chapter 6 Solutions

Understandable Statistics: Concepts and Methods

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Find the probability that within 2 years 47 or more fail.

Solution Summary: The author calculates the probability that within 2 years 47 or more fail. The binomial distribution is approximated to a normal distribution.

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Find the probability that within 2 years 47 or more fail.

Find the probability that within 2 years 58 or fewer fail.

Find the probability that within 2 years 15 or more succeed.

Find the probability that within 2 years fewer than 10 succeed.

Chapter 6 Solutions