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.