Question

In a certain population of birds, about 40 percent of the birds have a wingspan greater than 10 inches. Biologists studying the birds will create a simulation with random numbers to estimate the probability of finding 1 bird in a sample of 6 birds with a wingspan greater than 10 inches. Which of the following assignments of the digits 0 to 9 will model the population?

Answer 1

To simulate the probability of finding one bird with a wingspan greater than 10 inches in a sample of six, assign digits 0-3 to birds with larger wingspans and digits 4-9 for the remaining, giving a 40 percent representation as per the population data.

Step-by-step explanation:

To create a simulation for estimating the probability of finding 1 bird with a wingspan greater than 10 inches in a sample of 6 birds, we need to assign digits to represent the outcomes. Since 40 percent of the birds have a wingspan greater than 10 inches, we'll assign the random digits 0 to 9 in such a way that approximately 40 percent of them represent this category.

One way to do this is to assign 4 out of the 10 digits to represent birds with a wingspan greater than 10 inches. For example, we could have:

• Digits 0-3 represent birds with wingspan greater than 10 inches
• Digits 4-9 represent birds with a wingspan of 10 inches or less

This means if we draw a random number from 0 to 9, there is a 40% chance that it corresponds to a bird with a wingspan over 10 inches, which is consistent with the population statistics given.

Answer 2

Let the digits from 0 to 3 represent birds with a wingspan greater than 10 inches and the remaining digits represent birds with a wingspan less than or equal to 10 inches.

Step-by-step explanation:

The choices of the question is missing. Choices are:

a.Let the even digits represent birds with a wingspan greater than 10 inches and the odd digits represent birds with a wingspan less than or equal to 10 inches.

b.Let the digits 0 and 1 represent birds with a wingspan greater than 10 inches and the remaining digits represent birds with a wingspan less than or equal to 10 inches.

c.Let the digits from 0 to 2 represent birds with a wingspan greater than 10 inches and the remaining digits represent birds with a wingspan less than or equal to 10 inches.

d.Let the digits from 0 to 3 represent birds with a wingspan greater than 10 inches and the remaining digits represent birds with a wingspan less than or equal to 10 inches.

e.Let the digits from 0 to 4 represent birds with a wingspan greater than 10 inches and the remaining digits represent birds with a wingspan less than or equal to 10 inches.

The population proportion of birds which have a wingspan greater than 10 inches is 40% (0.40)

This proportion need to be reflected in the assignments of the digits 0 to 9 in order to model the population.

If the digits from 0 to 3 represent birds with a wingspan greater than 10 inches and the remaining digits represent birds with a wingspan less than or equal to 10 inches, this proporion is satisfied because 4 digits are assigned to birds with a wingspan greater than 10 inches and 6 digits are assigned to birds with a wingspan less than or equal to 10 inches.