### Problem Statement:If $ np \geq 5 $ and $ nq \geq 5 $, estimate $ P(\text{fewer than 4}) $ with $ n = 13 $ and $ p = 0.4 $ by using the normal distribution as an approximation to the binomial distribution; if $ np < 5 $ or $ nq < 5 $, then state that the normal approximation is not suitable.### Instructions:Select the correct choice below and, if necessary, fill in the answer box to complete your choice.#### Options:- **A.** $ P(\text{fewer than 4}) = \_\_\_\_ $ - Note: Round to four decimal places as needed. - **B.** The normal approximation is not suitable.---### Explanation of Concepts:- **Binomial Distribution:** A discrete probability distribution of the number of successes in a sequence of n independent experiments, where each experiment has a binary outcome (success/failure) with a constant probability of success, $ p $. - **Normal Approximation:** For a large number of trials $ n $, the binomial distribution $ B(n, p) $ can be approximated by a normal distribution $ N(np, \sqrt{npq}) $ if certain conditions, specifically $ np \geq 5 $ and $ nq \geq 5 $, are met. Here, $ q = 1 - p $. ---- **Given:** - $ n = 13 $ - $ p = 0.4 $ - **Calculate $ np $ and $ nq $:** - $ np = 13 \times 0.4 = 5.2 $ - $ nq = 13 \times 0.6 = 7.8 $ Since both conditions $ np \geq 5 $ and $ nq \geq 5 $ are satisfied, the normal approximation can be used.To find $ P(\text{fewer than 4}) $, convert the binomial variable to a normal variable and use the Z-score:- Mean ($ \mu $) = $ np $- Standard Deviation ($ \sigma $) = $ \sqrt{npq} $Calculate the Z-score and then find the corresponding probability from the standard

Identify the correct option to obtain the probability that X fewer than 4. The correct option is…

If np 25 and nq 25, estimate P(fewer than 4) with n= 13 and p = 0.4 by using the normal distribution as an approximation to the binomial distribution; if np< 5 or ng<5, then state that the normal approximation is not suitable. %3D %3D Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. P(fewer than 4)= (Round to four decimal places as needed.) O B. The normal approximation is not suitable.

If np 25 and nq 25, estimate P(fewer than 4) with n= 13 and p = 0.4 by using the normal distribution as an approximation to the binomial distribution; if np< 5 or ng<5, then state that the normal approximation is not suitable. %3D %3D Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. P(fewer than 4)= (Round to four decimal places as needed.) O B. The normal approximation is not suitable.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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