Question

The mean score of a test in a statistic class is 82; the variance is 25. The scores are normally distributed. Show Work

What percent of the students scored below 75?  

What percent of the students scored above 95?  

What percent of the students scored between 75 and 95?

Answer 1

Given data,

variance s² = 25

Standard deviation s = √25 = 5

mean   = 82

X~Normal(mean=82, s=5)

P(x < 75) = P((x - ) / sd < (75 - 82) / 5) = P(z< -1.4) = 0.0808

P(x > 95) = P((x - ) / sd > (95 - 82) / 5) = P(z >2.6) =1 - P(z<2.6) = 1 - 0.9953 = 0.0047

P(75 < x < 95)

= P( (75 - 82) / 5 < (x - ) / sd < (95 - 82) / 5 )

=P(-1.4 < z < 2.6)

= P(z<2.6) - P(z< -1.4)

= 0.9953 - 0.0808

=0.9145