Question

1. A given binomial distribution has a mean of 153.1 and a standard deviation of 18.2. Would a value of 187 be considered usual or

unusual? Why?
A. Unusual, because the result is less than the maximum usual value.
B. Usual, because the result is less than the minimum usual value.
C. Unusual, because the result is greater than the maximum usual value.
D. Usual, because the result is between the minimum and maximum usual values.

Answer 1

D. Usual, because the result is between the minimum and maximum usual values

Explanation:

Answer 2

Usual, because the result is between the minimum and maximum usual values.

Explanation:

To identify if the value is usual or unusual we're going to use the Range rule of thumbs which states that most values should lie within 2 standard deviations of the mean. If the value lies outside those limits, we can tell that it's an unusual value.

Therefore:

Maximum usual value: μ + 2σ

Minimum usual value: μ - 2σ

In this case:

μ = 153.1

σ = 18.2

Therefore:

Maximum usual value: 189.5

Minimum usual value: 116.7

Therefore, the value of 187 lies within the limits. Therefore, the correct option is D. Usual, because the result is between the minimum and maximum usual values.