Question

The 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, in a semester, most (95%) of the students spent on textbooks:a. between 215 and 255 dollars.b. between 195 and 275 dollars.c. between 175 and 295 dollars.d. less than 215 dollars or more than 255 dollars.e. above 235 dollars.

Answer 1

Answer:b. between 195 and 275 dollars

Explanation:

The Standard Deviation Rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean . The empirical rule is further illustrated below

68% of data falls within the first standard deviation from the mean.

95% fall within two standard deviations.

99.7% fall within three standard deviations.

From the information given, the mean is $235 and the standard deviation is $20.

95% of the amount spent by students on text books would fall within two standard deviations.

2 standard deviations = 2 × 20 = 40

235 - 40 = 195

235 + 40 = 275

Therefore, the amount spent is between between 195 and 275 dollars.

Answer 2

b. between 195 and 275 dollars.

Explanation:

The standard deviation rule, or the 68-95-99.7 rule, states that, for a normally distributed random variable X:

68% of the measures are within 1 standard deviation of the mean

95% of the measures are within 2 standard deviations of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean 235, standard deviation 20.

According to the Standard Deviation Rule, in a semester, most (95%) of the students spent on textbooks:

Between 235 - 2*20 = 195 dollars and 235 + 2*20 = 275 dollars.

So the correct answer is:

b. between 195 and 275 dollars.