Probabilities

Question

ACT Math Scores   In a recent year, the ACT  scores for the math portion of the test were normally distributed, with a mean of 21.1 and a standard deviation of 5.3. Find the probability that a randomly selected high school student who took the math portion of the ACT has a score that is (a) less than 16, (b) between 19 and 24, and (c) more than 26, and (d) identify any unusual events. Explain your reasoning

Answer 1

(a) To get the probability of those who scored less than 16%

Zx = (x-mean) /std dev

X is 16 mean is 21.1 and the std dev is 5.3

(16-21.1)/5.3 =-0.96

According to the table Px will be 0.16853

In percentage form the probability of students scoring less than 16 is 16.853%.

(b) To get the probability of those who scored between 19 and 24 will be done by getting

probability at 19 and probability at 24 then we subtract them.

(19-21.1)/5.3-0.396~0.4 p according to the table will be 0.34458 in percentage is 34.458%.

(24-21.1)/5.3=0.547~0.55 according to the table probability will be 0.70884 in percentage is 70.884%

So 70.884 % -34.458% = 36.426%

(c) More than 26

We'll get the probability of those who scored 26 and less then subtract the probability by 1 then get the percentage

(26-21.1) /5.3=0.9245 the probability at the table is 0.82121.

We subtract it from 1

So 1-0.82121=0.17879

In percentage is 17.879%

(d) The distribution is not normal as the values are not in increasing normally. But the distribution should be normal hence the wierd thing about it is that the probability between 19 and 24 is higher than 26.

(e)The distribution here is about scores. The higher the scores the higher the mean. But the distribution is unusual because the scores have been distributed in an unknown sequence. Hence not getting a normal distribution.