Standard normal table problems Part 2 If this helps These a

Standard normal table problems - Part 2

If this helps: These are hand calculated problems where you have to figure out if the random variable is X, Xbar, or Pbar. Then you have to label the top curve and shade the appropriate area. Shade the same area on the bottom Z curve and then use the appropriate Z formula and the standard normal table to find the answer. Problem: The hotel room rate in New York City is normally distributed with a mean of $292 per night. Assume that the standard deviation is unknown. If 22% of the New York City hotel room rates are more than $307 per night, what is the variance? Problem: Starbucks has found that 28% of customers purchase more than one cup of coffee per day from their shops. Suppose you randomly choose 185 of today\'s Starbucks customers. Find the probability that no less than 34% of them purchased more than one cup of coffee from Starbucks. **Please have the final answers be in at least 6 decimal places if possible. And I\'d greatly appreciate work being shown on how to solve them.

Solution

Hotel room rate...

As the left tailed area here is 1-0.22 = 0.78, the corresponding z score is, by table or technology,

z = 0.772193214

As

z = (x - u) / sigma

Then

sigma = (x - u)/z = (307-292)/0.772193214 = 19.42519013

Then

sigma^2 (variance) = 19.42519013^2 = 377.3380116 [ANSWER]

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