91Ó°ÊÓ

The data for a 5-mph cars test is provided.

The sample number of automobiles is n=10.

The car with no visible damage is represented by S (for success) and the car with damage is represented by F.

a.

Let x represents the number of successes.

The number of successes is 7.

The sample proportion of successes is computed as,

\(\begin{array}{c}\frac{x}{n} &=& \frac{7}{{10}}\\ &=& \dot 0.7\end{array}\)

Therefore, the sample proportion of successes is 0.7.

b.

The number of successes is 7.

Replacing each S with a 1 and each F with 0, the data is,

1 1 0 1 1 1 1 0 0 1 1

The sample mean is computed as,

\(\begin{array}{c}\bar x &=& \frac{{\sum {{x_i}} }}{n}\\ &=& \frac{{1 + 1 + 0 + ... + 1}}{{10}}\\ &=& \frac{7}{{10}}\\ &=& 0.7\end{array}\)

Thus, the sample mean is 0.7.

The value of the sample mean is the same as the sample proportion.

c.

The total number of cars is 25 when 15 cars are added to the sample.

The number of S’s that are to be included to give the sample proportion of 0.80 is computed as,

\(\begin{array}{c}\frac{x}{n} &=& 0.80\\x &=& \left( {0.80*n} \right)\\ &=& \left( {0.80*25} \right)\\ &=& 20\end{array}\)

Since, there were 7 S’s already, so, the additional S’s that are to be included to give the sample proportion as 0.80 is as follows,

\(20 - 7 = 13\)

Thus, there need to be 13 additional cars with no visible damage in sample of 15