Starbucks has found that 23% of customers purchase more than one cup of coffee p

Question

Starbucks has found that 23% of customers purchase more than one cup of coffee per day from their shops. Suppose you randomly choose 215 of today's Starbucks customers.

1) Find the probability that no less than 31% of them purchased more than one cup of coffee from Starbucks.

On the SAT, the average Writing score is 475 points and the average Mathematics score is 521 points. The standard deviation is 80 points on each part of the test. Now suppose 60 test takers are selected.

2) 10% of the time the sample average Mathematics score should be less than what?

The time it takes to bake a Betty Crocker Supermoist Fudge Cake is normally distributed with a mean of 44 minutes and a variance of 28 minutes^2. Let baking time, in minutes, be represented by random variable X.

3) P(x1 < X < 48) = 0.1230. Find x1

**Carry all decimals until you reach your answer, then round to four decimals.**

Explanation / Answer

Here, we treat the point estimate

u = point estimate = 0.23

and

sp = standard deviation = sqrt(p (1-p)/n) = sqrt(0.23*(1-0.23)/215) = 0.0287

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    0.31   
u = mean =    0.23      
          
s = standard deviation =  0.0287
          
Thus,          
          
z = (x - u) / s =    2.787
          
Thus, using a table/technology, the right tailed area of this is          
          P~( Z > 2.79 ) = 0.0026

PS : We are directed to solve only the first question when multiple questions are posted or the first 4 parts when multiple parts of the same question are posted.

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