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1. A popular retail store knows that the purchase amounts by its customers is a random variable that follows a normal distribution with a mean of $30 and a standard deviation of $9.
What are the two dollar amounts, equidistant from the mean of $30, such that 98% of all customer purchases are between these values?
AnswerMiddle 98% about mean is represented by 0.9800 area under the standard normal curve about mean
0.9800/2 = 0.4900 is the area on the left side of mean and 0.4900 is the area on the right side of mean
The z value corresponding to 0.4900 area on the left side is - 2.332 and the z score corresponding to 0.4900 area on the right side of mean is + 2.332
The two values are Mean +/- 2.32 SD
30 +/- 2.332*9
30 +/- 20.988
The first amount is 30 - 20.988 = $9.012 and
the second amount is 30 + 20.988 = $50.988
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A popular retail store knows that the purchase amounts by its customers is a random variable that follows a normal distribution with a mean of $30 and a standard deviation of $9.
What is the probability that a randomly selected customer will spend less than $15 at this store? Answer rounded to 4 decimal place.
Answerz(15) = (15-30)/9 = -15/9 = -1.6667
P(x < 15) = P(z < -1.6667) = normalcdf(-100,-1.6667) = 0.0478
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