Question

1)A normal distribution has μ = 24 and σ = 5.

(a) Find the z score corresponding to

x = 19.

(b) Find the z score corresponding to

x = 35.

(c) Find the raw score corresponding to

z = −2.

(d) Find the raw score corresponding to

z = 1.7.

2)Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.)

The area to the left of

z = −1.33 is  .

3)The method of tree ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution.

1257

1292

1243

1306

1268

1316

1275

1317

1275

(a) Use a calculator with mean and standard deviation keys to find the sample mean year x and sample standard deviation s. (Round your answers to the nearest whole number.)

x =
s =

(b) Find a 90% confidence interval for the mean of all tree ring dates from this archaeological site. (Round your answers to the nearest whole number.)

lower limit
upper limit

4)For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a random sample of 69 professional actors, it was found that 39 were extroverts.

(a) Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.)

(b) Find a 95% confidence interval for p. (Round your answers to two decimal places.)

lower limit
upper limit

Give a brief interpretation of the meaning of the confidence interval you have found.

     We are 95% confident that the true proportion of actors who are extroverts falls outside this interval.We are 5% confident that the true proportion of actors who are extroverts falls above this interval. We are 95% confident that the true proportion of actors who are extroverts falls within this interval.We are 5% confident that the true proportion of actors who are extroverts falls within this interval.

(c) Do you think the conditions np > 5 and nq > 5 are satisfied in this problem? Explain why this would be an important consideration.

     No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.

Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.    

Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.

No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.

5)Raul received a score of 74 on a history test for which the class mean was 70 with a standard deviation of 10. He received a score of 76 on a biology test for which the class mean was 70 with standard deviation 4. On which test did he do better relative to the rest of the class?

      biology test, history test, the same

6)Find z such that 6% of the standard normal curve lies to the left of z. (Round your answer to three decimal places.) z =  

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 52; σ = 17

P(40 ≤ x ≤ 47) =

7)Find z such that 8% of the standard normal curve lies to the right of z. (Round your answer to two decimal places.)
z =  

Answer 1

Solution:

Question 1)

Given: A normal distribution has and

Part a) We have to find the z score corresponding to x = 19.

z score formula:

Part b) Find the z score corresponding to x = 35

Part c) Find the raw score corresponding to z = −2.

We use following formula to find raw score:

Part d) Find the raw score corresponding to z = 1.7.