Question

1. What is the z-score corresponding to P66

2. What is the z-score corresponding to Q1

3. For a normal distribution with μ μ = 40 and σ σ = 3.1, determine P(x > 43.906).

4. For a standard normal distribution, determine the z-score, z0, such that P(z > z0) = 0.0931.

5. For a standard normal distribution, determine the z-score, z0, such that P(z < z0) = 0.9698.

6. From a normal distribution with μμ = 76 and σσ = 5.9, samples of size 46 are chosen to create a sampling distribution. In the sampling distribution determine P(74.399 < ¯xx¯ < 78.079).

7. From a normal distribution with μμ = 81 and σσ = 2.7, samples of size 48 are chosen to create a sampling distribution. In the sampling distribution determine the probability that a sample mean is between 81.109 and 81.398.

8. From a normal distribution with μμ = 47 and σσ = 5.8, samples of size 33 are chosen to create a sampling distribution. In the sampling distribution determine the probability that a sample mean is at least 45.768.

9. From a normal distribution with μμ = 34 and σσ = 3.7, samples of size 46 are chosen to create a sampling distribution. In the sampling distribution determine the probability that a sample mean is at most 35.107.

Please help with the following questions, would like to make sure I'm on the right track as for as my work shown.

Answer 1

1. For P66, z value is

Using z table we get z=0.412 such that

2. Here we need to find z such that

Using z table we get z=-0.674 such that

3. Here we need to find

As distribution is normal we can convert x to z

4. Here we need to find z0 such that P(z > z0) = 0.0931

Using z table we get P(z>1.322)=0.0931

So z value is 1.322