Question

ACT mathematics score for a particular year are normally distributed with a mean of 28 and a standard deviation of 2.4 points

Answer 1

Answer:

a.   0.1587

b.  0.8849

c.  0.1814

Step-by-step explanation:

a. Given that $\mu=28, \ \ \sigma=2.4$

-The probability a randomly selected score is greater than 30.4 is calculated as:

$P(X>30.4)=1-P(X30.4)=1-P(z$

Hence, the probability of a score greater than 30.4 is 0.1587

b. Given that $\mu=28, \ \ \ \sigma=2.4$

The probability a randomly selected score is less than 32.8 is calculated as:

$P(X$

Hence, the probability that a randomly selected score is less than 32.8 is 0.8849

c. The probability that a score is between 25.6 and 32.8 is calculated as follows:

$P(25.6$

Hence, the probability is 0.1814