Question

3. Quickstart company makes 12-volt car batteries. After many years of testing, the company knows that the average life of a quick start battery is normally distributed, with a mean if 45 months and a standard deviation of 8 months.

A. If Quickstart company guarantees a full refund on any battery that fails within 36 months after purchase, what of its batteries will the company expect to replace? (Round to a whole percentage)

B. If Quickstart company only wants to give refunds for up to 6% of their batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries? (Round to one decimal place as needed)

5. In a recent study reported on the Pew Research Blog, the mean age of people who use tablets is 28 years. Suppose the standard deviation is 13 years. Take a sample of size n=100. Find the probability that the sample mean age is more than 31 years.

6. In a certain population, 12% of people are left-handed. Suppose that you plan to randomly select 100 people and ask each person whether they are left-handed. Calculated each of the probabilities below using the normal distribution as an approximation to the binomial. (ROund probabilities to 4 decimal place).

A. Find the probability that among the 100 people, 19 or more are left-handed.

B. Based on your result from (a), is obtaining 19 left-handed people a significantly high number of left-handed people? Why or why not?

Answer 1

3. Quickstart company makes 12-volt car batteries. After many years of testing, the company knows that the average life of a quick start battery is normally distributed, with a mean if 45 months and a standard deviation of 8 months.

A. If Quickstart company guarantees a full refund on any battery that fails within 36 months after purchase, what of its batteries will the company expect to replace? (Round to a whole percentage)

Z value for 36, z =(36-45)/8 = -1.13

P( x <36) = P( z < -1.13) =0.1292

Or 12.92%

Required percentage = 13% ( rounded)

B. If Quickstart company only wants to give refunds for up to 6% of their batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries? (Round to one decimal place as needed)

Z value for lower 6% = -1.555

X=mean+z*sd = 45-1.555*8=32.56

=32.6 months

5. In a recent study reported on the Pew Research Blog, the mean age of people who use tablets is 28 years. Suppose the standard deviation is 13 years. Take a sample of size n=100. Find the probability that the sample mean age is more than 31 years.

Standard error = sd/sqrt(n) = 13/sqrt(100) =1.3

Z value for 31, z =(31-28)/1.3 =2.31

P( x >31) = P( z > 2.31)

=0.0104

6. In a certain population, 12% of people are left-handed. Suppose that you plan to randomly select 100 people and ask each person whether they are left-handed. Calculated each of the probabilities below using the normal distribution as an approximation to the binomial. (ROund probabilities to 4 decimal place).

Expectation = np = 12

Variance = np(1 - p) = 10.56

Standard deviation = 3.2496

A. Find the probability that among the 100 people, 19 or more are left-handed.

Z value for 19 with continuity correction. Z =(18.5-12)/3.2496 = 2.00

P( x>=19) = P(z >2.0)

=0.0228

B. Based on your result from (a), is obtaining 19 left-handed people a significantly high number of left-handed people? Why or why not?

The probability calculated above is 0.0228 which is less than 0.05. Therefore it is not significantly high number of left-handed people.