Question

5. The Curdle Dairy Co. wants to estimate the proportion p of customers that will purchase its new broccoli-flavored ice cream. Curdle wants to be 92% confident that they have estimated p to within .05. How many customers should they sample?

6. For a certain urban area, in a sample of 5 months, anaverage of 28 mail carriers were bitten by dogs each month. The standard deviation of the population is 3 mail carriers. Find the 90% confidence interval of the true mean number of mail carriers who are bitten by dogs each month.

Answer 1

Solution,

Given that,

5) =  1 - = 0.5

margin of error = E = 0.05

At 92% confidence level

= 1 - 92%

= 1 - 0.92 = 0.08

/2 = 0.04

Z/2 = Z0.04  = 1.751

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.751 / 0.05)2 * 05 * 0.5

= 306.60

sample size = n = 307

Given that,

6) Point estimate = sample mean = = 28

Population standard deviation =    = 3

Sample size = n = 5

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

Margin of error = E = Z/2 * ( /n)

= 1.645 * ( 3 /  5)

= 2.21

At 90% confidence interval estimate of the population mean is,

  ± E

28 ± 2.21

( 25.79 , 30.21)