A normal distribution has a mean of 40 and a standard deviat

A normal distribution has a mean of 40 and a standard deviation of 6.

1) What percent of the scores are between 22 and 58?

2) What score is needed to be in the bottom 42% of the distribution?

3) What percent of scores are below, x=45?

4) What percent of scores are above x=37?

Please explain best answer gets 5 Stars!!!

1.) P(22<X<58) = P((22-40)/6<Z<(58-40)/6) = P(-3<Z<3) = 0.9987 - (1-0.9987) = 0.9974 = 99.74%

2.) bottom 42% means z = -0.2

x = 40 + (-0.2)*(6) = 38.8

3.) P(X<45) = P(Z<(45-40)/6) = P(Z<0.83) = 0.7967 = 79.67%

4.) P(X>37) = P(Z>(37-40)/6) = P(Z>-0.5) = 1 -0.6915 = 0.3085 = 30.85%