Probability, Sampling Distributions, and Inference
2) The lifetimes of light bulbs of a particular type are normally distributed with a mean of 370 hours and a standard deviation of 5 hours. What percentage of bulbs has lifetimes that lie within 1 standard deviation of the mean on either side?
3) The amount of Jen's monthly phone bill is normally distributed with a mean of $60 and a standard deviation of $12. Fill in the blanks:
68% of her phone bills are between $______________ and $______________.
4) The amount of Jen's monthly phone bill is normally distributed with a mean of $50 and a standard deviation of $10. Find the 25th percentile.
5) The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches?
6) The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 88 inches, and a standard deviation of 10 inches. What is the likelihood that the mean annual precipitation during 25 randomly picked years will be less than 90.8 inches?
7) A final exam in Statistics has a mean of 73 with a standard deviation of 7.73. Assume that a random sample of 24 students is selected and the mean test score of the sample is computed. What percentage of sample means are less than 70?
8) A mean score on a standardized test is 50 with a standard deviation of 10. Answer the following
a. What scores fall between -1 and +1 standard deviation?
b. What percent of all scores fall between -1 and +1 standard deviation?
c. What score falls at +2 standard deviations?
d. What percentage of scores falls between +1 and +2 standard deviations?
The solution gives detailed steps on solving a series of questions on standard normal distribution and empirical rule.