1. ## probability z scores

7. Adrian's average bowling score is 174 and is normally distributed with a standard deviation of 35.
a) What Z-score corresponds to the following scores? i)80 ii)264 (already did it and i got .17 and 2.57)

b) In what percent of games does Adrian score less than 200 points? More than 200 points?

c) the top 10% of bolwers in Adrians league get to play in an all starr game. If the league average is 170 with a standard deviation of 22 points and is normally distributed what average score does Adrian need to have to obtain a spot in the all star game?

6) Out of 100 packages of jawbreakers 68 packages contain between 120 and 150. Use your knowledge of Normal distribution to estimate the average number of jawbreakers and standard deviation of the sample.

12) The weights of the 75 model planes at a local convention are normally distributed. The average weight is 4.4 kg with a standard deviation of 0.41kg.
a)How many planes have a mass less then 4kg?
b) how many planes would be disqualified if it were against the rules to have a plane with a mass of more than 5.5kg?
c) How many planes have a mass between 3.5kg and 5kg?

2. Originally Posted by Skoz
7. Adrian's average bowling score is 174 and is normally distributed with a standard deviation of 35.
a) What Z-score corresponds to the following scores? i)80 ii)264 (already did it and i got .17 and 2.57)

b) In what percent of games does Adrian score less than 200 points? More than 200 points?

Mr F says: Calculate Pr(X > 200) and multiply the answer by 100. I'd need to know how you've been taught to calculate probabilities if you need help doing the actual calculation. If you use tables for the standard normal distribution I'd need to know what values of z they have.

c) the top 10% of bolwers in Adrians league get to play in an all starr game. If the league average is 170 with a standard deviation of 22 points and is normally distributed what average score does Adrian need to have to obtain a spot in the all star game?

Mr F says: You need to find the value of a such that Pr(X > a) = 0.1. To do this, first find the value of z* such that Pr(Z > z*) = 0.1. Then $\displaystyle {\color{red}z* = \frac{a - 174}{35}}$. Substitute the value of z* and solve for a.

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12) The weights of the 75 model planes at a local convention are normally distributed. The average weight is 4.4 kg with a standard deviation of 0.41kg.
a)How many planes have a mass less then 4kg?

Mr F says: Calculate Pr(X < 4) and multiply the answer by 75.

b) how many planes would be disqualified if it were against the rules to have a plane with a mass of more than 5.5kg?

Mr F says: Calculate Pr(X > 5.5) and multiply the answer by 75.

c) How many planes have a mass between 3.5kg and 5kg?

Mr F says: Calculate Pr(3.5 < X < 5) = Pr(X < 5) - Pr(X < 3.5).
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