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Calculation of probability based on normal distribution, Z scores and Percentiles

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The amount of money that a family of four will spend at Kings Island, including the food and souvenirs, is $130 with a standard deviation of $12. Assume that this distribution is normal.

1. Find the probability that a particular family of four selected at random spends between $150 and $200?

2. What is the probability that the family spends less than $140?

3. What is the probability that the family spends more than $170?

4. What is the probability that the family spends between $130 and $190? (Draw a graph to illustrate your results)

5. Find the cost that represents the 50th percentile.

6. Find the cost that represents the 90th percentile.

7. 5% of the families spend below what value?

8. The top 5% of the families spend above what value?

9. Between what two values will the middle 50% of the families spend?

10. What percent of the families spend at least $120?

11. Use the empirical rule to determine the following:
A About 68% of the observations lie between what two values?
B About 95% of the observations lie between what two values?
C About 99% of the observations lie between what two values?

12. Use the standard normal distribution to determine the following
A 68% of the observations lie between what two values?
B 95% of the observations lie between what two values?
C 99% of the observations lie between what two values?

13. Discuss the differences in the results for question 12 and question 11

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The solution gives the details of calculation of probability, Z scores and percentiles based on a normal distribution.

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