Please show work1. The room rate for a hotel is normally distributed with a mean of $286 per night. Assume the standard deviation is unknown. If 21% of the hotel room rates are more than $326 per night, what is the variance?2. 33% of consumers read nutrition facts on products. For a sample of 270 consumers, what is the probability that between 81 and 100 of them read the nutrition facts?3. The average entry level wage for male college graduates is $20.12 per hour and $18.36 per hour for female college graduates. The standard deviation for male graduates is $3.89 and $3.18 for female graduates. Assume wages are normally distributed. If 31 female graduates are chosen, find the probability the sample average entry level wage is at least $19.704. The time it takes to bake a cake is normally distributed with a mean of 39 minutes and a variance of 26 minutes^2. Baking time in minutes is represented by random variable X. P(x1 < X < 44) = 0.1140. Find x1.5. Starbucks found that more than 22% of their customers purchase more than one cup of coffee per day from their shops. Suppose you randomly choose 205 of today's Starbucks customers . Find the probability that no less than 28% of them purchased more than one cup of coffee from Starbucks.6. On the SAT, the average writing score is 462 points and the average math score 519 points. The standard deviation is 84 points on each part of the test. 39 test takers are selected. 88% of the time, the sample average writing score should be less than what?
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