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Normal Probabilities

1- Surveying all drug stores in the Boston area, it was found that the average cost of a chocolate mint frappe is $30.50. The cost of a mint frappe population is normally distributed, with a standard deviation of $0.50. If I select a drug store in the Boston area randomly, what is the probability that the cost of is chocolate mint frappes is:
a) Between $3.25 and $3.50?
b) Greater than $3.75?
c) More than $3.60?
d) Less than $3.50?

2- The average credit card debt of college seniors is $3,262. If the debt is normally distributed with a standard deviation of $1,100. What is the probability that the senior owes:
a) At least $2000?
b) More than $4,200?
c) Between $2,900 and 4,200?

3- A quick walk at 4 miles per hour burns an average of 320 calories per hour. if the variable (calories) is normally distributed with a standard deviation of 9 calories. What is the probability that a person who walks at this rate for 1 hour will burn:
a) More than 300 calories?
b) Less than 311 calories?

4- The average annual salary for instructors at Quincy College is $24,393. If the salaries are normally distributed with a standard deviation of $4,362. What is the probability that:
a) An instructor selected randomly will have a salary less than $25,000?
b) Out of a sample of 36 instructors, the mean of the sample will be less than $25,000?

5- Children between the ages of 3 and 6 watch an average of 24 hours of TV per week. This time is normally distributed with a sigma of 3 hours.
a) What is the probability that the amount of television time watched by a randomly selected child from this population will be less than 25.3 hours?
b) What is the probability that the amount of time watched by a randomly selected child will be more than 27 hours?
c) If a sample of 20 children from this population is taken, what is the probability that the mean of the number of hours these children watch TV will be less than 25 hours?

Solution Summary

The solution provides step by step method for the calculation of probability using the Z score. Formula for the calculation and Interpretations of the results are also included.

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