Question

Harley-Davidson motorcycles make up 14% of all motorcycles registered in the US. You plan to interview an SRS of 500 motorcycles owners. How likely is your sample to contain 20% or less who own Harleys

Answer 1

To determine how likely it is for your sample of 500 motorcycle owners to contain 20% or less Harley-Davidson motorcycle owners, you can use sampling distribution.

Step-by-step explanation:

To determine how likely it is for your sample to contain 20% or less Harley-Davidson motorcycle owners, you can use sampling distribution.

First, find the standard deviation of the sampling distribution:

Standard deviation = sqrt( proportion * (1 - proportion) / sample size)

= sqrt(0.14 * (1 - 0.14) / 500) = sqrt(0.14 * 0.86 / 500) = sqrt(0.000238) = 0.0154

Next, find the z-score for the value of 20% using the formula:

Z = (sample proportion - population proportion) / standard deviation

= (0.2 - 0.14) / 0.0154 = 0.06 / 0.0154 = 3.8967

Lastly, find the probability using the z-score:

Probability = P(Z <= 3.8967) = 0.9999

Therefore, there is a 99.99% likelihood that your sample will contain 20% or less Harley-Davidson motorcycle owners.

Answer 2

0.00005 probability or 0.005%