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**Question:** Suppose that 60% of college students own a smartphone manufactured by Apple. If a random sample of 200 college students is selected, use the normal distribution to approximate the probability that the number of students in the sample owning a smartphone made by Apple will be less than 105. Is it reasonable to use the normal approximation here? **Explanation:** To determine if it is reasonable to use a normal approximation, we need to check the conditions for the normal approximation of the binomial distribution. Typically, the normal approximation is suitable when both \( np \) and \( n(1-p) \) are greater than or equal to 10, where \( n \) is the sample size and \( p \) is the probability of success. In this case: - \( n = 200 \) - \( p = 0.60 \) - \( np = 200 \times 0.60 = 120 \) - \( n(1-p) = 200 \times 0.40 = 80 \) Both \( np \) and \( n(1-p) \) exceed 10, so it is reasonable to use the normal approximation.

**Question:** Suppose that 60% of college students own a smartphone manufactured by Apple. If a random sample of 200 college students is selected, use the normal distribution to approximate the probability that the number of students in the sample owning a smartphone made by Apple will be less than 105. Is it reasonable to use the normal approximation here? **Explanation:** To determine if it is reasonable to use a normal approximation, we need to check the conditions for the normal approximation of the binomial distribution. Typically, the normal approximation is suitable when both \( np \) and \( n(1-p) \) are greater than or equal to 10, where \( n \) is the sample size and \( p \) is the probability of success. In this case: - \( n = 200 \) - \( p = 0.60 \) - \( np = 200 \times 0.60 = 120 \) - \( n(1-p) = 200 \times 0.40 = 80 \) Both \( np \) and \( n(1-p) \) exceed 10, so it is reasonable to use the normal approximation.

MATLAB: An Introduction with Applications
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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**Question:** Suppose that 60% of college students own a smartphone manufactured by Apple. If a random sample of 200 college students is selected, use the normal distribution to approximate the probability that the number of students in the sample owning a smartphone made by Apple will be less than 105. Is it reasonable to use the normal approximation here? **Explanation:** To determine if it is reasonable to use a normal approximation, we need to check the conditions for the normal approximation of the binomial distribution. Typically, the normal approximation is suitable when both \( np \) and \( n(1-p) \) are greater than or equal to 10, where \( n \) is the sample size and \( p \) is the probability of success. In this case: - \( n = 200 \) - \( p = 0.60 \) - \( np = 200 \times 0.60 = 120 \) - \( n(1-p) = 200 \times 0.40 = 80 \) Both \( np \) and \( n(1-p) \) exceed 10, so it is reasonable to use the normal approximation.
Transcribed Image Text:**Question:** Suppose that 60% of college students own a smartphone manufactured by Apple. If a random sample of 200 college students is selected, use the normal distribution to approximate the probability that the number of students in the sample owning a smartphone made by Apple will be less than 105. Is it reasonable to use the normal approximation here? **Explanation:** To determine if it is reasonable to use a normal approximation, we need to check the conditions for the normal approximation of the binomial distribution. Typically, the normal approximation is suitable when both \( np \) and \( n(1-p) \) are greater than or equal to 10, where \( n \) is the sample size and \( p \) is the probability of success. In this case: - \( n = 200 \) - \( p = 0.60 \) - \( np = 200 \times 0.60 = 120 \) - \( n(1-p) = 200 \times 0.40 = 80 \) Both \( np \) and \( n(1-p) \) exceed 10, so it is reasonable to use the normal approximation.
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