Insurance companies have determined that US males between th

Insurance companies have determined that US males between the ages of 16 and 24, drive an average of 10,718 miles each year with a standard deviation of 3763 miles. Assume the data is normally distributed. For a randomly selected male in that age group, find the probability that he drives less than 12,000 miles per year. 23. A company that manufactures sleeping bags says that the average amount down in an adult sleeping bag is 32 oz. with a standard deviation of 0.9 cz. is the probability that a bag chosen at random has more than 33.2 oz. of down of 24. The heights of six-year old girls are normally distributed with a mean of 117.80 cm and a standard deviation of 5.52 cm. Find the probability that a randomly selected six-year girl has a height between 117.80 cm and 120.56 cm. 25. The average heating bill for a residential area is $123 for the month of November with a standard deviation of $8. If the amounts of the heating bills are normally distributed, find the probability that the average bill for a randomly selected resident is more than $125 26. An IQ test has a mean of 100 with a standard deviation of 15. What is the probability that a randomly selected adult has an IQ between 85 and 115? deviation of 1 hour. What percent of adults spend more than 6 hours per week on their home computer? 27. The average adult spends 5 hours per week on a home computer, with a standard

Solution

22.

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    12000      
u = mean =    10718      
          
s = standard deviation =    3763      
          
Thus,          
          
z = (x - u) / s =    0.340685623      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   0.340685623   ) =    0.633329869 [ANSWER]

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23.

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    33      
u = mean =    32      
          
s = standard deviation =    0.9      
          
Thus,          
          
z = (x - u) / s =    1.111111111      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.111111111   ) =    0.133260263 [ANSWER]

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