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In the population of female students, motivation scores follow a normal distribution with an average of 29 and a standard deviation of 4.3. A random sample of female students is to be taken. They are all asked to answer the motivation questionnaire so that their motivation scores can be determined.
-If the sample size is 20, what is the probability that the mean score of the female students in the sample will fall below 27?
A)

Question

Use the following information for questions:
 In the population of female students, motivation scores follow a normal distribution with an average of 29 and a standard deviation of 4.3. A random sample of female students is to be taken. They are all asked to answer the motivation questionnaire so that their motivation scores can be determined.
-If the sample size is 20, what is the probability that the mean score of the female students in the sample will fall below 27?
A) < 0.0001
B) 0.0005
C) 0.0188
D) 0.3192

Quizplus · Accepted Answer

To find the probability that the mean score of the sample falls below 27, we use the formula for the standard error of the mean: SE = σ / √n, where σ is the population standard deviation and n is the sample size. Here, SE = 4.3 / √20 ≈ 0.961. We then calculate the z-score for a mean of 27: z = (27 - 29) / 0.961 ≈ -2.08. Looking up this z-score in a standard normal distribution table or using a calculator gives a probability of about 0.0188.

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