A variable has a normal distribution with a mean of 170 and

A variable has a normal distribution with a mean of 170 and a standard deviation of 10.

5. The most extreme 5% of score are all below _____ or above ____.

6. What percent of scores are below x=183?

7. What score is needed to be in to 1% of the distribution?

mu =170

sigma = 10

Z score for 95% = 1.96 both sides

Hence X should be 170-1.96*10, 170+1.96*10

=(150.4, 189.6)

The most 5% extreme are either below 150.4 or above 189.6

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P(X<183) = P(Z<1.3) = 0.9032

Hence 90.32%

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To be in 1% of the distribution

z score should be below -2.58 or above 2.58

Hence x should be below 170-(2.58*19.6) or above 170+2.58*19.6

below 119.432 or above 220.568