Provide an appropriate response. In order to efficiently bid on a contract, a contractor wants to be 95% confident that his error is less than two hours in estimating the average time it takes to install tile flooring. Previous contracts indicate that the standard deviation is 4.5 hours. How large a sample must be selected?

a. 19

b. 4

c. 5

d. 20

d. 20

Step-by-step explanation:

Standard deviation is 4.5

Margin error for the problem is 2 hours

Probability 95%, that means that the siginficance level α is 1 - p

α = 1 - 0.95 = 0.05

margin of error (ME) can be defined as follows

ME = Z (α/2) * standard deviation / √n

Where n is the sample size

Z (0.05/2) = Z (0.025)

Using a z table Z = 1.96

Now, replacing in the equation and find n

2 = 1.96 * 4.5 / √n

2 = 8.82/√n

√n = 8.82/2

√n = 4.41

n = 4.41^2

n = 19.44 ≈ 20