1)A state legislator wishes to survey registered voters in her district to see what proportion is aware on her position on using state funds to build a convention center in New York. She is unwilling to make any preliminary assumption about this proportion.

a)What sample size is necessary in order to be 80% confident that the sample proportion is with + 4% of the true proportion?

b)Suppose 300 registered voters are surveyed and 75 are found to be aware of her position. Find a 98% confidence interval for the true proportion of registered voters that are aware of her position.

2)The operator of a telephone exchange wishes to estimate the mean length of a

phone call.A sample of 25 calls yields a mean of 9.1 minutes with a standard

deviation of 4 minutes.

a)Construct a 95% confidence interval for the mean duration of a call.

b)If the operator would like to estimate the mean length of calls to within .5

minutes with a 99% confidence, how large should her sample size be?

3)A random sample of 3 is taken from a lot of 10 items. If the lot contains 4 defective items,

a)What is the probability of getting two or more defective items? (Do not bother to carry out the calculations)

b)What is the probability of getting no defective item?

c)What is the probability of getting at least one defective items?