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wrote...
Posts: 227
2 weeks ago
According to Gallup, about 33% of Americans polled said they frequently experience stress in their daily lives. Suppose you are in a class of 45 students.

a. What is the probability that no more than 12 students in the class will say that they frequently experience stress in their daily lives? (Make sure to identify the sampling distribution you use and check all necessary conditions.)
b. If 20 students in the class said they frequently experience stress in their daily lives, would you be surprised? Explain, and use statistics to support your answer.
Textbook 

Stats: Modeling the World


Edition: 4th
Authors:
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wrote...
Posts: 245
2 weeks ago
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a. We want to find the probability that no more than 12 students in the class will say that they frequently experience stress. This is the same as asking the probability of finding less than 26.7% of "stressed" students in a class of 45 students.

Check the conditions:

1. 10% condition: 45 students is less than 10% of all students who could take the class

2. Success/failure cond.: np = 45(0.33) = 14.85, nq = 45(0.67) = 30.15, which both exceed 10

We can use the N(0.33 = 0.070) to model the sampling distribution.
We need to standardize the 26.7% and then find the probability of getting a z-score less than or equal to the one we find: z = = -0.90
P( < 0.267) = P(z < -0.90) = 0.1841, so the probability is about 18.4% that no more than 12 students will say that they frequently experience stress in their daily lives.
b. From part a, we can use N(0.33, 0.070) to model the sampling distribution. Twenty students is about 44.4% of the class. This is about 1.63 standard deviations above what we would expect, which is not a surprising result.
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2 weeks ago
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