MS 150 Statistics Fall 2003 Test Two Name:

  1. The diagram below depicts three normal curves:
    s33_normalcurves (11K)

    1. _______ Which curve has the largest mean?
    2. _______ Which curve has the largest standard deviation?
    3. _______ What is the mean for curve A?
    4. _______ What is the mean for curve B?
    5. _______ What is the mean for curve C?
    6. _______ Estimate the standard deviation for curve A
    7. _______ Estimate the standard deviation for curve B
    8. _______ Estimate the standard deviation for curve C

asashoryu (103K) kyokutenho (98K) takanonami (97K) wakanosato (82K)

  1. Thirty-seven Japanese sumo wrestlers were measured for the holding force of their hands. The sumo wrestlers had a mean holding force of 170 pounds with a standard deviation of 24 pounds. The holding force values were normally distributed.
    1. n = __________ What is the sample size n?
    2. = __________ What is the mean ?
    3. s = __________ What is the standard deviation s?
    4. z = __________ Convert x = 194 to a z value.
    5. z = __________ Convert x = 218 to a z value.
    6. p(194 < x < 218) = __________ Find the probability (the area under the normal curve between the two z values above) that a sumo wrestler has a holding force of between 194 pounds and 218 pounds.
    7. __________ Use the percentage calculated in the previous question and the sample size above to determine how many sumo wrestlers have a holding force between 194 pounds and 218 pounds.
    8. z = __________ Convert x = 150 to a z value.
    9. z = __________ Convert x = 200 to a z value.
    10. p(150 < x < 200) = __________ Find the probability (the area under the normal curve between the two z values above) that a sumo wrestler has a holding force of between 150 pounds and 200 pounds.
    11. __________ Use the percentage calculated in the previous question and the sample size above to determine how many sumo wrestlers have a holding force between 150 pounds and 200 pounds.
    12. __________ What is the holding force x above which there is a 25% probability a wrestler has that holding force? Hint: this is an inverse problem and is asking for the x value for the uppermost 25% of the area.
Statistic or Parameter Symbol Equations Excel
Calculate a z value from an x z = standardize.gif (905 bytes) =STANDARDIZE(x, , s)
Calculate an x value from a z x = s z + = s*z+
Find a probability p from a z value =NORMSDIST(z)
Find a z value from a probability p =NORMSINV(p)

normal (3K) left_to_z_small (2K)