1. The time it takes to bake a Betty Crocker Supermoist Fudge Cake is normally d

Question

1. The time it takes to bake a Betty Crocker Supermoist Fudge Cake is normally distributed with a mean of 36 minutes and a variance of 28 minutes^2. Let baking time, in minutes, be represented by random variable X. (Round to four decimals points)

P(x1<X<41)=0.1200 Find x1. (Remember the label.)

2. On the SAT, the average Writing score is 489 points and the average Mathematics score is 528 points. The standard deviation is 93 points on each part of the test. Now suppose 39 test takers are selected. (answer to 4 decimals)

90% of the time the sample average Writing score should be less than what? (remember the label)

3. Starbucks has found that 25% 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 30% of them purchased more than one cup of coffee from Starbucks. (answer to four decimal points)

Explanation / Answer

1)

here std deviation =(28)1/2 =5.2915

P(x1<X<41) =0.12

P((41-36)/5.2915)-P(x1-36)/5.2915)=0.12

P(Z<0.94)-P(x1-36)/5.2915) =0.12

P(x1-36)/5.2915) =0.8276-0.12 =0.7076

hence (x1-36)/5.2915 =0.5464

x1 =38.8912

2)

for 90th percentile ; z score =1.2816

therefore corresponding score =mean +Z*std deviation =508.0848

3)

here mean=       = 489.000 std deviation   == 93.0000 sample size       =n= 39 std error=x=/n= 14.8919

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