Question

Horn lengths of Texas longhorn cattle are normally distributed. The mean horn spread is 60 inches with a standard deviation of 4.5 inches.

Calculate the range of horn lengths for the middle 99.7% of Texas longhorn cattle.

A.
51 in.–60 in.

B.
51 in.–69 in.

C.
60 in.–73.5 in.

D.
46.5 in.–73.5 in.

Answer 1

D. 46.5 in.–73.5 in

Which statement describes data that is negatively skewed?

B. The majority of the data is to the right of the mean.

For the following data set, calculate the percentage of data points that fall within one standard deviation of the mean and compare the result to the expected percentage of a normal distribution.

{8, 12, 27, 32, 45, 57, 61, 73, 82, 94}

B. 50%; This percentage is lower than expected in a normal distribution.

What is the probability the spinner will land on a dotted region?

D. 50%

A target is made of a blue square inside of a red square. The blue square has an area of 64 square units, and the red square has an area of 196 square units.

Assuming it hits the target, what is the probability that a dart will land in the red region?

C. 0.67

Answer 2

The empirical rule says that roughly 99.7% of the population is within 3 standard deviations of the mean.

Start at the center 60 which is the mean. Add on 3 standard deviations

60 + 3*4.5 = 73.5

and subtract off 3 standard deviations from the mean

60 - 3*4.5 = 46.5

So roughly 99.7% of the population of cattle has horn lengths between 46.5 inches and 73.5 inches

Answer: Choice D. 46.5 in - 73.5 in