Question

A researcher records the following body mass index (BMI) scores for a group of participants: 28.4 ± 1.6 ( M ± SD). Participants who score between 25 and 30 on this scale are categorized as overweight. What percentage of participants fell in this overweight category?a) 0.4834.

b) 0.1753.
c) 0.8413.
d) 0.8247.

Answer 1

D) 0.8247

Explanation:

The first thing is to look for a normal distribution table that gives us the values of Z.

Now the percentage of people with BMI between 25 and 30 is given as follows:

P (25 <x <30) = P {[(25 -28.4) /1.6] <Z <P {[(30 -28.4) /1.6]

The value of 25 would be 25 minus the arithmetic mean divided by the standard deviation.

The value of 30 would be 30 minus the arithmetic mean divided by the standard deviation.

When solving that we have the following way:

P {-2.125 <Z <1]

This can be expressed as follows:

P (Z <1) - [1 - P (Z <2.13)]

Now we turn to the normal distribution table and find that:

P (Z <1) = in table 0.8413

P (Z <2.13) = in table 0.9834

When replacing the values we have that:

0.8413 - (1 - 0.9834) = 0.8247

Which means that the percentage of person with that BMI is 0.8247