Question 1: The economic policy institute reports that the average entry level w

Question

Question 1: The economic policy institute reports that the average entry level wage for male college graduates is $20.70 per hour and for female college graduates is $18.04 per hour. The standard deviation for male graduates is $3.80 and for female is $3.09. Assume wages are normally distributed. If 25 female graduates are chosen, find the probability the sample average entry-level wage is at least $19.03.

Question 2: 12% if individuals insured by All-driver automobile insurance company have received at least one traffic ticket. For a sample of 170 insured individuals, what is the probability that between 14 and 26 of them have received at least one ticket?

Question 3: the hotel room rate in New York City is normally distributes with a mean of $238 per night. Assume that the standard deviation is unknown. If 29% of the New York City hotel room rates are more than $268 per night, what is the variance? please label

Question 4: On the SAT, the average writing score is 459 points and the average mathematics score is 537 points. The standard deviation is 69 points on each part of the test. Now suppose 39 test takers are selected. 93% of the time the sample average writing score should be less than what? please label

Question 5: the time it takes to bake a Betty Croker Super moist Fudge Cake is normally distributed with a mean of 35 minutes and a variance of 26 minutes ^2. Let baking time, in minutes, be represented by random variable X. please label

P(x1<1<X<39)=0.0900. Find x1

Question 6:According to the national center of education statistics, 65% of Texas students are eligible to receive free or reduced-priced lunches. Suppose you randomly choose 275 Texas students. Find the probability that no more than 73% of them are eligible to receive free or reduced-price lunches.

Explanation / Answer

Ans:

2)n=170,p=0.12

Normal approximation to binomial:

mean=np=20.4

std deviation=sqrt(np(1-p))=sqrt(20.4*0.88)=4.24

P(14<=X<=26)

z=(14-20.4)/4.24=-1.51

z=(26-20.4)/4.24=1.32

P(-1.51<=z<=1.32)=P(z<=1.32)-P(z<=-1.51)=0.9066-0.0655=0.8411

3)P(Z>=z)=0.29

P(Z<=z)=1-0.29=0.71

z=0.5534

0.5534=(268-238)/std dev

std dev=30/0.5534=54.21

Variance=2938.72

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