Question

1a) In one math course, the scores on one particular 25-point quiz are well-modeled by a normal distribution with mean value of 17 points and standard deviation of 2.5 points.Rounding to two digits past the decimal point, and including a percentage symbol in your answer (with no spaces): What percentage of students received a score of 20 points or higher on the quiz?

1b) Rounding to two digits past the decimal point, and including a percentage symbol in your answer (with no spaces):In the Standard Normal Distribution, what percentage of area under the curve lies between the values of -1.55 and 1.73 on the horizontal axis?

1c) Rounding to four digits past the decimal point: In the model N(7, 3) what horizontal axis value should we use as a lower bound, in order to produce a right-tail area amount of 38% ?

Answer 1

a.

μ=17, σ=2.5

We need to compute Pr(X≥20). The corresponding z-value needed to be computed is:

Therefore, we get that

The percentage of students received a score of 20 points or higher on the quiz is 11.51%.

b

μ=0, σ=1

We need to compute Pr(−1.55 ≤ X ≤ 1.73).

Therefore, we get:

The percentage of area under the curve lies between the values of -1.55 and 1.73 on the horizontal axis is 89.76.

c.

horizontal axis value should we use as a lower bound, in order to produce a right-tail area amount of 38% is 7.53.