Question

The distribution of the amount of money spent by students on textbooks in a semester is approximately normal in shape with a mean of 349 and a standard deviation of 24. According to the standard deviation rule, approximately 95% of the students spent between ____$ and ____$ on textbooks in a semester.

Question 12

Type numbers in the boxes.

1 points

The distribution of IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 16. According to the standard deviation rule, ____% of people have an IQ between 52 and 148. Do not round.

Question 13

Type numbers in the boxes.

10 points

The distribution of IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 13. According to the standard deviation rule, only _____% of people have an IQ over 139.

Question 14

Type numbers in the boxes.

10 points

The distribution of the amount of money spent by students on textbooks in a semester is approximately normal in shape with a mean of: μ= 310 and a standard deviation of: σ= 36.

According to the standard deviation rule, almost 2.5% of the students spent more than what amount of money on textbooks in a semester? ____

Answer 1

Emiprical rule: From the 68-95-99.7 Rule, 68% of values fall within 1 standard deviation of mean. 95% of values fall within 2 standard deviation of mean and 97.7% of values fall within 3 standard deviation of mean.

Question 11:

Here we have

According to standard deviation rule, 95% data values lies within 2 standard deviations of mean. So required interval is:

Question 12:

Here we have

So,

According to standard deviation rule, 99.7% data values lies within 3 standard deviations of mean.

Answer: 99.7%

Question13:

Here we have

So,

According to standard deviation rule, 99.7% data values lies within 3 standard deviations of mean.

That is percentage of data values lie between 100 and 139 is 99.7% / 2 = 49.85%

That is percentage right to 139 is : 50% - 49.85% = 0.15%

Answer: 0.15%

Question 14:

Here we have

So,

According to standard deviation rule, 95% data values lies within 2 standard deviations of mean.

That is percentage of data values lie between 310 and 382 is 95% / 2 = 47.5%

That is percentage right to 382 is : 50% - 47.5% = 2.5%

Answer: 382