Math 136 Introduction to Statistics Name:
Quiz 5A Normal Distributions & Sampling ID Num:
Sketch and shade relevant parts to find probabilities for FULL CREDIT.
1. (7 points) In 2020 it is believed that the average smartphone price was $580 with a standard
deviation of $300. Assume the distribution of phone smartphone prices is normally distributed.
(a) Sketch and shade the relevant region to find the probability that a randomly selected smart-
phone sale in 2020 cost less than 200.
(b) Sketch and shade the relevant region to find the probability that a randomly selected smart-
phone sale in 2020 was between $500 and $800.
(c) Would observing a smart phone sale over $1,000 be unusual? Explain.
Please go on to the next page. . .
2. (7 points) In 2020 it is believed that the average smartphone price was $580 with a standard
deviation of $300. Assume the distribution of phone smartphone prices is normally distributed.
Suppose that we now take a sample of 30 smarphones sold in 2020.
(a) Describe the sampling distribution of the mean in our sample of 30 smartphones.
(b) Sketch and shade the relevant region to find the probability that the sample average will be
less than $500.
(c) Answer this without computing probabilities. Would the probability of getting a mean
value for the smart phone sales over $1,000 be higher or lower than what you find in Problem
1 part (c)? Explain.
It may be helpful to sketch.
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