On an IQ test with a mean of 100 and a standard deviation of 15, John’s Z score
ID: 3172656 • Letter: O
Question
On an IQ test with a mean of 100 and a standard deviation of 15, John’s Z score is 1.25. What is John’s score on the IQ test?
In a chemistry mid-term exam Mary’s score corresponds to a z score of 2. What percentage of students performed better than Mary? What percentage of students did Mary outperform? Use the empirical rule.
The most commonly used IQ test has a mean of 100 and a standard deviation of 15. Based on this test and the empirical rule, what percent of the population qualifies for membership in Mensa (to join you have to have an IQ of 130 or greater)?
Find the probability that the number obtained when a die is rolled is an odd number.
Explanation / Answer
Z-score = (X -mean)/sd
1.25 = (X - 100)/15
hence X = 100+15*1.25 = 118.75
z-score = 2
In statistics, the 68–95–99.7 rule is a shorthand used to remember the percentage of values that lie within a band around the mean in a normal distribution with a width of two, four and six standard deviations, respectively;
hence (100-95)/2 = 2.5 % performed better than Mary.
Similarlly 97.5 % Mary outformed.
z-score = (130-100)/15 =2
by help of previous question ,2.5 % qualifies for membership in Mensa