Question

The grades of a statistics midterm are normally distributed with a mean of 70 and a standard deviation of 2. Without using a calculator, what is the probability that a student will receive a grade between 74 and 76? 4.30% 2.15% 34.12% 13.6%

Answer 1

Answer:

.13.5%

Step-by-step explanation:

The probability that a student will receive a grade between 74 and 76 is calculated as follows:

µ+2σ=70+2(2)=70+4=74

µ+3σ=70+3(2)=70+6=76

From the above empirical rule it can be observed that 13.5% of observations fall in between 1 and 2 standard deviations above the mean.

Therefore, the probability that a student will receive a grade between 74 and 76 is 13.5%.

Thus, the correct options is A.13.5%.