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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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    https://brainmass.com/statistics/normal-distribution/calculation-of-probability-based-on-normal-distribution-z-scores-and-percentiles-111636

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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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