Problem 1 till 3 are from section 5.4 and Problem 4 till 7 are from section 5.5

Please read section 5.4 before you answer problems 1-3. Problem

1. Suppose we know that the birth weight of babies is normally distributed with mean 3500g and standard deviation 500g.

(1A). What is the probability that a baby is born with weight less than 3100g? Hint answer the below problem a and b then you are done.

a. Find the z-score, and construct the standard normal distribution density curve, then shade your seeking area.

b. Find the probability.

(1B). If 25 new born babies are randomly selected, what is the probability that the 25 babies are born that their mean weigh less than 3100g? Hint answer the below problem a and b then you are done.

a. Find the z-score, and construct the standard normal distribution density curve, then shade your seeking area.

b. Find the probability

Problem 2. The life of a certain type of engine is normally distributed with a mean of 10 years, and a standard deviation of 1.5 years.

(2A). If one engine is randomly selected, what is the probability that the life of this engine is between 8 and 13 years? Hint answer the below problem a and b then you are done.

a. Find the z-score, and construct the standard normal distribution density curve, then shade your seeking area.

b. Find the probability

(2B). If 20 engines are randomly selected, what is the probability that the mean life of these 20 engines is between 8 and 13 years? Hint answer the below problem a and b then you are done.

a. Find the z-score, and construct the standard normal distribution density curve, then shade your seeking area.

b. Find the probability

Problem 3. A company pays its employees an average hourly wage of $36.25 with a standard deviation of $6.50. If 36 employees are randomly selected, what is the probability that their mean wage is more than $23.22?

Approximating a binomial distribution: In problem number four and five, a binomial experiment is given. Determine whether you can use a normal distribution to approximate the binomial distribution. If you can, find the mean and standard deviation. If you cannot explain why.

Problem 4. A survey of US adults found that 37% have been to Court. You randomly select 30 US adults and ask them whether they have been to court.

Problem 5. A survey of use adults found that 11% think that Congress is a good reflection of Americans views. You randomly select 35 US adults and ask them whether they think that Congress is a good reflection of Americans views.

Approximating binomial probability: In problem number six and seven, determine whether you can use a normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and a sketch their graphs. If you cannot, explain why and use a binomial distribution to find the indicated probabilities.

Problem 6. A survey of US adults found that 69% of those who text on cell phones receive spam or unwanted messages you randomly select 100 U.S adults who text on cell phones. Find the probability that the number who receive spam or unwanted message is

A) exactly 70,

B) at least 70,

C) fewer than 70.

Problem 7. A survey of US adults found that 67% off was raising the Medicaid eligibility age from 65 to 67. You randomly select 80 US adults and ask them how they feel about raising the Medicare eligibility age from 65 to 67. Find the probability that the number oppose raising the age is

A) At least 65

B) Exactly 50

C) More then 60