# BTM 8104 BTM8104 Week 3 Data File 3 (NCU)

BTM8104 Week 3 Data File 3 (NCU)

**Chapter Five**

1) If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, what percentage of light bulbs have a life less than 2500 hours?

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 25^{th} 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

**Chapter Six**

1) For the following questions, would the following be considered “significant” if its probability is less than or equal to 0.05?

2) If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT. What is the probability of getting at least one head?

3) A sample space consists of 64 separate events that are equally likely. What is the probability of each?

4) A bag contains 4 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue?

5) The data set represents the income levels of the members of a country club. Estimate the probability that a randomly selected member earns at least $98,000.

6) Suppose you have an extremely unfair coin: The probability of a head is ¼ and the probability of a tail is ¾. If you toss the coin 32 times, how many heads do you expect to see?

7) The following table is from the Social Security Actuarial Tables. For each age, it gives the probability of death within one year, the number of living out of an original 100,000 and the additional life expectancy for a person of that age. Determine the following using the table: