The scores on a particular exam are normally distributed with a mean of 75 points out of 100 points, and a standard deviation of 7 points.
(a) what percentage of the scores fall between 68 and 82 points?
(b) what percentage of the scores fall between 54 and 96 points?

you!

From a score x we calculate z=(x - μ)/σ and look up the result in the standard normal table.

x=68, z=(68-75)/7 = -1

x=82, z=(82-75)/7 = 1

Nice, we don't have to look anything up.  By the 68-95-99.7 rule 68% of the scores fall between plus or minus one standard deviation from the mean.

a) 68%

x=54, z=(54-75)/7 = -3

x = 96, z=(96-75)/7 = 3

Same rule, plus or minus three sigma gives 99.7% of the scores

b) 99.7%

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i