Question

He distribution of the amount of money spent by students for textbooks in a semester is approximately normal in shape with a mean of $235 and a standard deviation of $20. according to the standard deviation rule, how much did almost all (99.7%) of the students spend on textbooks in a semester?

Answer 1

Almost all (99.7%) of the students spent between $175 and $295 on textbooks in a semester.

Step-by-step explanation:

To determine how much almost all (99.7%) of the students spent on textbooks in a semester, we can use the standard deviation rule for a normal distribution. According to the rule, approximately 99.7% of the values fall within 3 standard deviations of the mean.

Given that the mean is $235 and the standard deviation is $20, we can calculate the range by multiplying the standard deviation by 3 and adding/subtracting the result to/from the mean. So, the range is ($235 - $20 * 3) to ($235 + $20 * 3), which is $175 to $295.

Therefore, almost all (99.7%) of the students spent between $175 and $295 on textbooks in a semester.

Answer 2

The standard deviation rule tells us that for distributions that have the normal shape, approximately 99.7% of the observations fall within 3 standard deviations of the mean.

Here, Mean = 235 and Standard deviation= 20

So, 3 standard deviation below the mean= Mean- 3 standard deviation

= 235 - (3× 20)

= 235 - 60 = 175

and 3 standard deviation above the mean= Mean + 3 standard deviation

= 235 + (3× 20)

= 235 + 60 = 295

So, almost all (99.7%) of the students spent between $175 and $295 on textbooks in a semester.