Statistics All Sum Solution - 20008

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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 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

  1. What scores fall between –1 and +1 standard deviation?
  2. What percent of all scores fall between –1 and +1 standard deviation?
  3. What score falls at +2 standard deviations?
  4. 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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