QuestionIn a group of 348 students, how many will have an IQ within 1 standard deviation (15) of the mean (100)?

Studdy Solution

STEP 1

Assumptions1. The mean IQ is100. . The standard deviation is15.
3. The number of students tested is348.
4. We are using the empirical rule, which states that approximately68% of values in a normal distribution fall within1 standard deviation of the mean.

STEP 2

First, we need to find the percentage of students who will fall within1 standard deviation of the mean. According to the empirical rule, this is approximately68%.

STEP 3

Now, we need to calculate the number of students who fall within this range. We can do this by multiplying the total number of students by the percentage.
$Number\, of\, students = Total\, number\, of\, students \\times Percentage$

STEP 4

Now, plug in the given values for the total number of students and the percentage to calculate the number of students.
$Number\, of\, students =348 \\times68\%$

STEP 5

Convert the percentage to a decimal value.
$68\% =0.68$ $Number\, of\, students =348 \\times0.68$

STEP 6

Calculate the number of students.
$Number\, of\, students =348 \\times0.68 =237$ Approximately237 students will fall within1 standard deviation of the mean.

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