Question

According to the College Board, SAT mathematics scores from the 2014 school year for high school students in the United States were normally distributed with a mean of 513 and a standard deviation of 120. Use a standard normal table such as this one to determine the probability that a randomly chosen high school student who took the SAT in 2014 will have a mathematics SAT score between 400 and 750 points.

Answer 1

Answer:

80.25%

Explanation:

Data provided in the question

$X \sim N (513,120)$

Mean = 513

Standard deviation = 120

Now

$P(400 < x < 750) = P (\frac{400 - 513}{120}$

After solving this

= P (-0.9417 < Z < 1.975)

= P (-0.9417 < Z < 0) + P (0 < Z < 1.975)

= 0.3264 + 0.4761

or by apply the Z table or excel command

Like this

NORMSDIST(1.98) - NORMSDIST(-0.94)

= 0.9761 - 0.1736

= 80.25%

Hence the probability is 80.25%