Question

Record Examination) are normally distributed with a mean of 555 and a standard

deviation of 110. Use the 68-95-99.7 Rule to find the percentage of people taking the test who score below 335.
The percentage of people taking the test who score below 335 is

Answer 1

2.5%

Explanation:

You want the percentage below 335 if the distribution is normal with a mean of 555 and a standard deviation of 110, using the empirical rule.

Z score

The z-score of 335 is ...

Z = (X -µ)/σ

Z = (335 -555)/110 = -220/110 = -2

Distribution

The empirical rule tells you that 95% of the distribution is between Z = -2 and Z = 2. That is, 5% of the distribution is evenly split between the tails Z < -2 and Z > 2. Half that value is in each tail.

P(X < 335) = 5%/2 = 2.5%

The percentage of people taking the test who score below 335 is 2.5%.

<95141404393>