The manager of a paint supply store wants to estimate the actual amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer. the manufacturer's specifications state that the standard deviation of the amount of paint is equal to 0.02 gallon. a random sample of 50 cans is selected, and the sample mean amount of paint per 1-gallon can is 0.998 gallon. complete parts (a) through (d).

a. construct a 95% confidence interval estimate for the population mean amount of paint included in a 1-gallon can.

b. on the basis of these results, do you think the manager has a right to complain to the manufacturer? why?

a 1-gallon paint can containing exactly 1-gallon of paint lies 95% confidence interval.

c. must you assume that the population amount of paint per can is normally distributed here? explain.

d. construct a 90% confidence interval estimate. how does this change your answer to part (b)?

how does this change your answer to part (b)?

a 1-gallon paint can containing exactly 1-gallon of paint lies 90% confidence interval. the manager right to complain to the manufacturer.

a. 95% confidence interval estimate for the population mean amount of paint included in a 1-gallon can is 0.998±0.0055

b.  No, because a 1-gallon paint can containing exactly 1-gallon of paint lies within the 95% confidence interval.

c. Yes.  The population amount of paint per can is assumed normally distributed, because confidence interval calculations assume normal distribution of the parameter.

d. 90% confidence interval is 0.998±0.0046. The answer in b. didn't change; 1-gallon paint can containing exactly 1-gallon of paint lies within the 90% confidence interval. The manager doesn't have a right to complain to the manufacturer.

Step-by-step explanation:

Confidence Interval can be calculated using M±ME where

M is the sample mean amount of paint per 1-gallon can (0.998 gallon)

ME is the margin of error from the mean

And margin of error (ME) can be calculated using the equation

ME= where

Then ME=≈0.0055

95% confidence interval is 0.998±0.0055

90% confidence interval can be calculated similary, only z statistic is 1.64.

ME=  ≈0.0046

90% confidence interval is 0.998±0.0046

c

step-by-step explanation:

$3720

step-by-step explanation:

taxable income = $31000

as per the 2018-2019 us tax bracket, the tax rate is 12% for an individual whose taxable income is between $9,526 to $38,700.

so, the tax to be paid by him = 12% of 31000

= 0.12 * 31000     [12% converted to decimal as 0.12]

= $3720