Question

2. Speeds of the fastest cars at a race location are normally distributed with a mean of 64.8 mph, and standard deviation 8.9 mph. Find the speed that separates the slowest 6% of vehicles from the rest. Round your answer to two decimal places.

3. Refrigerators of a certain type have lifetimes that are normally distributed with mean 675 hours and standard deviation 44.5 hours. Find the lifetime (in hours) that would separate the longest 1.5% from the rest. Round your answer to one decimal place.

4. The board of education that administers the CPA examination in a certain state found that the mean score on the test was 595 and the standard deviation was 72. If the board wants to set the passing score so that only the best 12% of all applicants pass, what is the passing score? Assume that the scores are normally distributed. Round your answer to one decimal place.

5. Scorecard of children’s in elementary school are normally distributed with a mean of 100 and a standard deviation of 15. Find the IQ score separating the top 12.5% from the others. Round your answer to two decimal places.

Answer 1

Solution:-

2) Given that,

mean = = 64.8

standard deviation = = 8.9

Using standard normal table,

P(Z < z) = 6%

= P(Z < z) = 0.06  

= P(Z < -1.55) = 0.06

z = -1.55

Using z-score formula,

x = z * +

x = -1.55 * 8.9 + 64.8

x = 51.01

3) Given that,

mean = = 675

standard deviation = = 44.5

Using standard normal table,

P(Z > z) = 1.5%

= 1 - P(Z < z) = 0.015  

= P(Z < z) = 1 - 0.015

= P(Z < z ) = 0.985

= P(Z < 2.17 ) = 0.985  

z = 2.17

Using z-score formula,

x = z * +

x = 2.17 * 44.5 + 675

x = 771.6

4) Given that,

mean = = 595

standard deviation = = 72

Using standard normal table,

P(Z < z) = 12%

= P(Z < z) = 0.12  

= P(Z < -1.17) = 0.12

z = -1.17

Using z-score formula,

x = z * +

x = -1.17 * 72 + 595

x = 510.8

5) Given that,

mean = = 100

standard deviation = = 15

Using standard normal table,

P(Z > z) =12.5 %

= 1 - P(Z < z) = 0.125  

= P(Z < z) = 1 - 0.125

= P(Z < z ) = 0.875

= P(Z < 1.15 ) = 0.875  

z = 1.15

Using z-score formula,

x = z * +

x = 1.15 * 15 + 100

x = 117.25