MS 150 Statistics Fall 2003 Test Two Name:

1. The diagram below depicts three normal curves:
   
   
   
   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

2. 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. µ = __________ What is the mean µ?
   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(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)