Question

Caffeine content in a 5-ounce cup of brewed coffee ranges from 60 to 180 mg, depending on brew time, coffee bean type, and grind. (a) Use the midrange to estimate the measure of centre. Midrange 120mg (b) Use the Empirical Rule to estimate the standard deviation. Standard deviation 20mg (c) Why is the assumption of a normal, bell-shaped distribution important in making these estimates? Because we can estimate the mean with the midrange. Because we can estimate the mean with the standard deviation. Because we can estimate the standard deviation with the median.

Answer 1

the desired estimated mean caffeine content is 120mg.

Step-by-step explanation:

a) Determine the desired mean using the midrange of the data.

The formula to determine the midrange is

Now substitute the desired Maximum and minimum values in the given formula. Therefore, the desired midrange is determine as follows:

Therefore, the desired estimated mean caffeine content is 120mg.

b)

Evaluation of the desired standard deviation using the empirical rule

According to the desired rule of empirical, we predict that if the data is from normal distribution, than interval

c)

According to empirical rule almost all the values are in the limits. As the estimated mean caffeine content is 120mg, Let the estimate of standar

Answer 2

a) 120

b) 30

c) Because we can estimate the mean with the mid range

Step-by-step explanation:

a)

The mid range can be calculated as

Mid range=(minimum value+maximum value)/2

Mid range=(60+180)/2

Mid range=240/2

Mid range=120

b)

The standard deviation can be computing by dividing the range by 4.

Range=maximum-minimum

Range=180-60

Range=120

Standard deviation=120/4

Standard deviation=30

c)

Assumption of normality is important because mean and standard deviation can be estimated from mid range using normality.