The scores on an exam are normally distributed, with a mean of 84 and a standard deviation of 6. what percent of the scores are less than 90?

Question

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

Answer 1

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:

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.

Answer 2

If we go by the standard bell curve, then 34% of scores are within one standard deviation above the mean. 90 is 6 units above 84 making it within one standard deviation. Therefore 84% of scores are below 90.