Patagonia is an outdoor American clothing and gear company and was founded in 1973. The average price of a Patagonia jacket is $202 and the standard deviation is $21. Suppose that 6 Patagonia jackets are randomly selected. Round answers to 4 decimal places. a. What is the distribution of ? T - N b. For the group of 6, find the probability that the average price is between $208 and $216. c. Find the third quartile for the average Patagonia jacket price for this sample size. $ (round to the nearest cent) d. For part b), is the assumption that the distribution is normal necessary? O YesO No

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Patagonia is an outdoor American clothing and gear company and was founded in 1973. The average price of a Patagonia jacket is $202 and the standard deviation is $21. Suppose that 6 Patagonia jackets are randomly selected. Round answers to 4 decimal places.

a. What is the distribution of \( \bar{x} \)? \( \bar{x} \sim N \left( \_\_, \_ \right) \)

b. For the group of 6, find the probability that the average price is between $208 and $216. \_\_\_\_

c. Find the third quartile for the average Patagonia jacket price for this sample size. $ \_\_\_\_ 
   ( \text{round to the nearest cent} )

d. For part b), is the assumption that the distribution is normal necessary? ◯ Yes ◯ No
Transcribed Image Text:Patagonia is an outdoor American clothing and gear company and was founded in 1973. The average price of a Patagonia jacket is $202 and the standard deviation is $21. Suppose that 6 Patagonia jackets are randomly selected. Round answers to 4 decimal places. a. What is the distribution of \( \bar{x} \)? \( \bar{x} \sim N \left( \_\_, \_ \right) \) b. For the group of 6, find the probability that the average price is between $208 and $216. \_\_\_\_ c. Find the third quartile for the average Patagonia jacket price for this sample size. $ \_\_\_\_ ( \text{round to the nearest cent} ) d. For part b), is the assumption that the distribution is normal necessary? ◯ Yes ◯ No
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