Question

1. The time it takes a student to cycle to school is normally distributed with a mean of 15 minutes and a variance of 2. The student has to be at school at 8.00a.m. At what time should the student leave her house so that she will be late only 4% of the time?

2. In a study for Health Statistics, it was found that the mean height of female 20-25 years old was 64.1 inches. If height is normally distributed with a standard deviation of 2.8 inches.
a)Determine the height required to be in the top 10% of all 20-25 years old females.
b)A “one-size-fits all” robe is being designed that should fit 90% of 20-25 years old females; what heights constitute the middle 90% of all 20-25 years old females?

3. The compressive strength of cement is assumed to be normally distributed with a mean of 8000 kilograms per sq cm and a standard deviation of 200 kilograms per sq. cm.
a)Find the probability that the strength is less than 8200 kg per sq. cm
b)Find the probability that the strength is between 7500 and 7700 kg per sq. cm
c)Determine the value for which the probability that the strength of cement is below this value is 90%.

Answer 1

1. Z = (score-mean)/SD

Variance = SD^2

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the Z score related to that proportion. Remember that the Z score will be negative. Plug in the values in the above equation and solve for the score.

2 & 3. Follow a similar processes for these values.