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**Mathematics Sum Solution**

** **

**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

- What scores fall between –1 and +1 standard deviation?
- What percent of all scores fall between –1 and +1 standard deviation?
- What score falls at +2 standard deviations?
- What percentage of scores falls between +1 and +2 standard deviations?

**Chapter Six: (6)**

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

**1. **Is it “significant” to get a 12 when a pair of dice is rolled?

2. Assume that a study of 500 randomly selected school bus routes showed that 480 arrived on time. Is it “significant” for a school bus to arrive late?

**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.

112,000 126,000 90,000 133,000 94,000

112,000 98,000 82,000 147,000 182,000

86,000 105,000 140,000 94,000 126,000

119,000 98,000 154,000 78,000 119,000

**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?

Solution Description

bulbs will have a life less than 2500 hours.

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