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(a) A box contains 7 balls. Two are numbered 3, three is numbered 4, and two are numbered 5. The balls are mixed and one is selected at random. After a ball is selected, its number is recorded. Then it is replaced. The probability distribution table is given below. Number on ball (X) 3 4 Probability P(X) 2/7 3/7 2/7 If the experiment is repeated many times, find the variance and standard deviation of the numbers on the balls. (b) Public Opinion reported that 5% of Americans are afraid of being alone in a house at night. If a random sample of 20 Americans is selected, find these probabilities. (1). There are exactly 4 people in the sample who are afraid of being alone at night. (). There are at most 3 people in the sample who are afraid of being alone at night.

(a) A box contains 7 balls. Two are numbered 3, three is numbered 4, and two are numbered 5. The balls are mixed and one is selected at random. After a ball is selected, its number is recorded. Then it is replaced. The probability distribution table is given below. Number on ball (X) 3 4 Probability P(X) 2/7 3/7 2/7 If the experiment is repeated many times, find the variance and standard deviation of the numbers on the balls. (b) Public Opinion reported that 5% of Americans are afraid of being alone in a house at night. If a random sample of 20 Americans is selected, find these probabilities. (1). There are exactly 4 people in the sample who are afraid of being alone at night. (). There are at most 3 people in the sample who are afraid of being alone at night.

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 50E: Flexible Work Hours In a recent survey, people were asked whether they would prefer to work flexible...
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(a) A box contains 7 balls. Two are numbered 3, three is numbered 4, and two are numbered 5. The balls are mixed and one is selected at random. After a ball is selected, its number is recorded. Then it is replaced. The probability distribution table is given below. Number on ball (X) Probability P(X) 2/7 3/7 2/7 If the experiment is repeated many times, find the variance and standard deviation of the numbers on the balls. (b) Public Opinion reported that 5% of Americans are afraid of being alone in a house at night. If a random sample of 20 Americans is selected, find these probabilities. (1). There are exactly 4 people in the sample who are afraid of being alone at night. (i1). There are at most 3 people in the sample who are afraid of being alone at night.
Transcribed Image Text:(a) A box contains 7 balls. Two are numbered 3, three is numbered 4, and two are numbered 5. The balls are mixed and one is selected at random. After a ball is selected, its number is recorded. Then it is replaced. The probability distribution table is given below. Number on ball (X) Probability P(X) 2/7 3/7 2/7 If the experiment is repeated many times, find the variance and standard deviation of the numbers on the balls. (b) Public Opinion reported that 5% of Americans are afraid of being alone in a house at night. If a random sample of 20 Americans is selected, find these probabilities. (1). There are exactly 4 people in the sample who are afraid of being alone at night. (i1). There are at most 3 people in the sample who are afraid of being alone at night.
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