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A pharmaceutical company gives 29 subjects a new antihistamine, and gives another 29 subjects a placebo (a pill containing no medicine). Afterwards, 8 of the 58 subjects are selected at random to be studied further. Let random variable X = the number of subjects among the 8 people selected who were given the placebo. a. Find the probability mass function f(x) = P(X=x), and sketch its histogram. b. Find P(X= 4). What does this number represent? c. Find P(X24). What does this number represent? d. Find P(Xs7). What does this number represent?

A pharmaceutical company gives 29 subjects a new antihistamine, and gives another 29 subjects a placebo (a pill containing no medicine). Afterwards, 8 of the 58 subjects are selected at random to be studied further. Let random variable X = the number of subjects among the 8 people selected who were given the placebo. a. Find the probability mass function f(x) = P(X=x), and sketch its histogram. b. Find P(X= 4). What does this number represent? c. Find P(X24). What does this number represent? d. Find P(Xs7). What does this number represent?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A pharmaceutical company gives 29 subjects a new antihistamine, and gives another 29 subjects a placebo (a pill containing no medicine). Afterwards, 8 of the 58 subjects are selected at random to be studied further. Let random variable X = the number of subjects among the 8 people selected who were given the placebo. a. Find the probability mass function f(x) = P(X =x), and sketch its histogram. b. Find P(X= 4). What does this number represent? c. Find P(X24). What does this number represent? d. Find P(Xs7). What does this number represent? Using the hypergeometric probability distribution model, set up an expression that can be used to find a single ordered pair in the probability mass function f(x) = P(X =x).
Transcribed Image Text:A pharmaceutical company gives 29 subjects a new antihistamine, and gives another 29 subjects a placebo (a pill containing no medicine). Afterwards, 8 of the 58 subjects are selected at random to be studied further. Let random variable X = the number of subjects among the 8 people selected who were given the placebo. a. Find the probability mass function f(x) = P(X =x), and sketch its histogram. b. Find P(X= 4). What does this number represent? c. Find P(X24). What does this number represent? d. Find P(Xs7). What does this number represent? Using the hypergeometric probability distribution model, set up an expression that can be used to find a single ordered pair in the probability mass function f(x) = P(X =x).
Using the hypergeometric probability distribution model, set up an expression that can be used to find a single ordered pair in the probability mass function f(x) = P(X = x). D-x fx) = P(X = x) = (Simplify your answers.) a. Find the probability mass function f(x) = P(X = x). The probability mass function f(x) is (Type an ordered pair. Use a comma to separate answers as needed. Round to three decimal places as needad) Let x the number of defective pedometers among the 8 units tested, and let y fx) Choose the correct histogram below. OA. OB. OC. OD. AY 044 04- Av 0.4 03 0.3 02 03 03 02 02f 0.1 02 0.1 0.1 01 012345678 012345678 01234 5678 01234567 S b. Find P(X= 4). P(X= 4)= (Round to three decimal places as needed.) What does P(X= 4) represent? O A. This is the probability that at least 4 of the 8 subjects selected received the placebo. O B. This is the probability that the fourth of the 8 subjects selected received the placebo. OC. This is the probability that only 4 out of the total 58 subjects received the placebo. O D. This is the probability that exactly 4 of the 8 subjects selected received the placebo. c. Find P(X2 4). P(X24) = (Round to three decimal places as needed.) What does P(X2 4) represent? O A. This is the probability that exactly 4 of the 8 subjects selected received the placebo. O B. This is the probability that at least 4 out of the total 58 subjects received the placebo. O C. This is the probability that some number of subjects after the fourth of the 8 subjects selected received the placebo. O D. This is the probability that at least 4 of the 8 subjects selected received the placebo. d. Find P(Xs7). P(Xs7)= (Round to three decimal places as needed.) What does P(Xs7) represent? O A. This is the probability that exactly 7 of the 8 subjects selected received the placebo. O B. This is the probability that some number of subjects before the seventh of the 8 subjects selected received the placebo. OC. This is the probability that at most 7 of the 8 subjects selected received the placebo. O D. This is the probability that at most 7 out of the total 58 subjects received the placebo.
Transcribed Image Text:Using the hypergeometric probability distribution model, set up an expression that can be used to find a single ordered pair in the probability mass function f(x) = P(X = x). D-x fx) = P(X = x) = (Simplify your answers.) a. Find the probability mass function f(x) = P(X = x). The probability mass function f(x) is (Type an ordered pair. Use a comma to separate answers as needed. Round to three decimal places as needad) Let x the number of defective pedometers among the 8 units tested, and let y fx) Choose the correct histogram below. OA. OB. OC. OD. AY 044 04- Av 0.4 03 0.3 02 03 03 02 02f 0.1 02 0.1 0.1 01 012345678 012345678 01234 5678 01234567 S b. Find P(X= 4). P(X= 4)= (Round to three decimal places as needed.) What does P(X= 4) represent? O A. This is the probability that at least 4 of the 8 subjects selected received the placebo. O B. This is the probability that the fourth of the 8 subjects selected received the placebo. OC. This is the probability that only 4 out of the total 58 subjects received the placebo. O D. This is the probability that exactly 4 of the 8 subjects selected received the placebo. c. Find P(X2 4). P(X24) = (Round to three decimal places as needed.) What does P(X2 4) represent? O A. This is the probability that exactly 4 of the 8 subjects selected received the placebo. O B. This is the probability that at least 4 out of the total 58 subjects received the placebo. O C. This is the probability that some number of subjects after the fourth of the 8 subjects selected received the placebo. O D. This is the probability that at least 4 of the 8 subjects selected received the placebo. d. Find P(Xs7). P(Xs7)= (Round to three decimal places as needed.) What does P(Xs7) represent? O A. This is the probability that exactly 7 of the 8 subjects selected received the placebo. O B. This is the probability that some number of subjects before the seventh of the 8 subjects selected received the placebo. OC. This is the probability that at most 7 of the 8 subjects selected received the placebo. O D. This is the probability that at most 7 out of the total 58 subjects received the placebo.
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