Please show all of the work. I have limited time to get this answer.

Hi Laurie, hope this helps -

A normal distribution means that 68% of the values lie within 1 standard deviation(σ) of the mean(μ), 95% lie within 2σ, and 99.7 lie within 3σ as seen on a bell curve.

In your question:

A normal distribution means that 68% of the values lie within 1 standard deviation(σ) of the mean(μ), 95% lie within 2σ, and 99.7 lie within 3σ as seen on a bell curve.

In your question:

μ= 84

σ=6

A score of 90 is 1σ above the μ. Therefore Pr(x≤μ+σ) = 50 + 68/2 = 50+34=84% of the values are less than 90.