Homework Help: Type 2 error, 2 questions

1. Mar 11, 2010

Pinto09

1) A car producer claims a certain type of car is fuel-saving and can be driven 25 miles/gallon and a st dev of 2.8 miles/gallon.
An analyst wants to test this claim and wants a 1% risk of concluding the statement is false when it in fact is true. He chooses 30 observations.

Calculate the probability for type 2 error if the true mean is 24?

I tried:
X-bar critical = 26.32 and 23.68 and got P(-0.62 < Z < 4.53) = F(0.62)

But the book's answer is 0.64?

2)
A company considers launching a new product if the proportion of customers who will buy it is at least 0.2.
A sample of 100 was taken. The null hypothesis (P =0.2) is rejected if the smaple proprtion is at least o.27.

The following requirements must be met:
P(not rejecting H0) = at least 99% if true proportion is 0.17
P(rejecting H0) = at least 99% if true proportion is 0.27

e) What sample size is required (at least)?
Book: 365
f) What is the significance level?
Book: 17%

How do you solve this??