For any normally distributed population, 190. On the average, how many individua

Question

For any normally distributed population,

190. On the average, how many individual outcomes out of 50,000 fall between 1.2 standard deviations below, and 2.1 standard deviations above the mean?

191. About what percent of the population is above z=-0.65?

A normally distributed population has mean 80 and standard deviation 6.

192. What is the probability that a randomly chosen member of the population will fall between 75 and 82?

193. Out of 1000 individual scores, how many fall between 80 and 90?

194. What is the probability that a randomly chosen score will be less than 71?

195. What is the 90th percentile score?

196. The top 5% (as determined by a standardized test) of high school senior math students will receive $2000 scholarships. Is scores are normally distributed with mean 180 and standard deviation 8, what cutoff score determines the winners?

Explanation / Answer

190) for

hence on average 50000*0.8671 =~43355 fall between those values,

191)

P(Z>-0.65)= 0.7422

192)

probability that a randomly chosen member of the population will fall between 75 and 82

193)

hence indivduals who have score between those values =1000*0.4522 ~ 452

194)

195) for 90th percentile ; z=1.2816

hence corresponding value =mean+z*std deviation =87.69

196) for top 5% ; z =1.6449

hence corresponding cut off score =180+1.6449*8 =193.16

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