Suppose we have a random variable X where, for the values k =0, …, 10, the associated probabilit

Name: Problem 2, Chapter 4: AP Statistics with 6 Practice Tests
Uploaded: 2021-04-11T17:16:44-08:00
Duration: 2 min 31 s
Channel: Manisha Sarker
Description: Suppose we have a random variable X where, for the values k =0, …, 10, the associated probabilities are ( 10 k )(0.37)^k(0.63)^10-k . What is the mean of X ? (A) 0.37 (B) 0.63 (C) 3.7 (D) 6.3 (E) None of the above

step 1 In this problem, we are going to find the mean of a random variable. Now the random variable x i

Question

Suppose we have a random variable $X$ where, for the values $k$ $=0, \ldots, 10,$ the associated probabilities are $\left(\begin{array}{c}10 \\ k\end{array}\right)(0.37)^{k}(0.63)^{10-k} .$ What is the mean of $X ?$ (A) 0.37 (B) 0.63 (C) 3.7 (D) 6.3 (E) None of the above

   Suppose we have a random variable $X$ where, for the values $k$ $=0, \ldots, 10,$ the associated probabilities are $\left(\begin{array}{c}10 \\ k\end{array}\right)(0.37)^{k}(0.63)^{10-k} .$ What is the mean of $X ?$
(A) 0.37
(B) 0.63
(C) 3.7
(D) 6.3
(E) None of the above

AP Statistics with 6 Practice Tests

Martin Sternstein 11th Edition

Chapter 4, Problem 2

Instant Answer

Solved by Expert Manisha Sarker

04/11/2021

Step 1

37)^{k}(0.63)^{10-k} .$ This is the form of a binomial distribution. Show more…

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Suppose we have a random variable $X$ where, for the values $k$ $=0, \ldots, 10,$ the associated probabilities are $\left(\begin{array}{c}10 \\ k\end{array}\right)(0.37)^{k}(0.63)^{10-k} .$ What is the mean of $X ?$ (A) 0.37 (B) 0.63 (C) 3.7 (D) 6.3 (E) None of the above

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Key Concepts

Expected Value (Mean) of a Binomial Distribution

The expected value of a binomial distribution is the long-run average number of successes calculated as the product of the number of trials and the probability of success (np). This value represents the central tendency or mean of the distribution.

Binomial Distribution

A binomial distribution models the number of successes in a fixed number of independent trials, each with an identical probability of success. It is characterized by two parameters, the number of trials (n) and the probability of success (p), and is used to calculate probabilities of achieving a specified number of successes.

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