Question

# One way of checking the effect of undercoverage, nonresponse, and other sources of error in a...

One way of checking the effect of undercoverage, nonresponse, and other sources of error in a sample survey is to compare the sample with known facts about the population. About 14% of American adults are black. The numbers X of blacks in a random sample of 1700 adults should therefore vary with the binomial (n = 1700, p = 0.14) distribution.

(a) What are the mean and standard deviation of X? (Round your standard deviation to three decimal places.)

mean = 238 blacks

SD = 14.307 blacks

(b) Use the Normal approximation to find the probability that the sample will contain between 223 and 253 blacks. (Round your answer to four decimal places.)

P(223 ≤ X ≤ 253) =

I only need the part to (b) answered. I couldn't figure out this portion of the answer.

Solution :

Given that ,

mean = = 238 blacks

standard deviation = = 14.307 blacks

P(223 x 253)

= P[(223 - 238 / 14.307 ) (x - ) / (253 - 238 / 14.307) ]

= P(-1.05 z 1.05)

= P(z 1.05) - P(z -1.05)

Using z table,

= 0.8531 - 0.1469

= 0.7062

#### Earn Coins

Coins can be redeemed for fabulous gifts.

##### Need Online Homework Help?

Most questions answered within 1 hours.