Find each of the following probabilities for a normal distribution.
a. p(21.80 , z , 0.20)
b. p(20.40 , z , 1.40)
c. p(0.25 , z , 1.25)
d. p(20.90 , z , 20.60)

16. in2014, average of m 5 245 (actually 0.245 but we will avoid
the decimals). of course, the batting average varies from game to game, but assuming that the distribution of bat- ting averages for 162 games is normal with a standard deviation of s 5 40 points, answer each of the following.

a. if you randomly select one game from 2014, what
is the probability that the team batting average was
over 300?
b. if you randomly select one game from 2014, what
is the probability that the team batting average was under 200?

17. iq test scores are standardized to produce a normal distribution with a mean of m 5 100 and a standard deviation of s 515. find the proportion of the popula- tion in each of the following iq categories.

a. genius or near genius: iq over 140
b. very superior intelligence: iq from 120 to 140
c. average or normal intelligence: iq from 90 to 109

18. the distribution of scores on the sat is approxi-
mately normal with a mean of m 5 500 and a standard
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deviation of s 5 100. for the population of students who have taken the sat:

a. what proportion have sat scores less than 400? b. what proportion have sat scores greater than 650? c. what is the minimum sat score needed to be in
the highest 20% of the population?
d. if the state college only accepts students from the
top 40% of the sat distribution, what is the mini- mum sat score needed to be accepted?