- The diagram below depicts three normal curves:

- _______ Which curve has the largest mean?
- _______ Which curve has the largest standard deviation?
- _______ What is the mean for curve A?
- _______ What is the mean for curve B?
- _______ What is the mean for curve C?
- _______ Estimate the standard deviation for curve A
- _______ Estimate the standard deviation for curve B
- _______ Estimate the standard deviation for curve C

- 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.
- n = __________ What is the sample size n?
- µ = __________ What is the mean µ?
- s = __________ What is the standard deviation s?
- z = __________ Convert x = 194 to a z value.
- z = __________ Convert x = 218 to a z value.
- 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.
- __________ 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.
- z = __________ Convert x = 150 to a z value.
- z = __________ Convert x = 200 to a z value.
- 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.
- __________ 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.
- __________ 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(x, µ, s) |

Calculate an x value from a z | x | = s z + µ | = s*z+µ |

Find a probability p from a z value | =NORMSDIST(z) | ||

Find a z value from a probability p | =NORMSINV(p) |