Need answer (by 11:00 p.m. EST) 2. Exercise 7.11 METHODS AND APPLICATIONS Suppos

Question

Need answer (by 11:00 p.m. EST)

2. Exercise 7.11 METHODS AND APPLICATIONS Suppose that we will randomly select a sample of 72 measurements from a population having a mean equal to 18 and a standard deviation equal to 9. (a) Describe the shape of the sampling distribution of the sample mean Do we need to make any assumptions about the shape of the population? Why or why not? Normally distributed , yes -|, because the sample size is , because the sample size is arge b) Find the mean and the standard deviation of the sampling distribution of the sample mean (Round your R answer to 1 decimal place.) 18 1.7 Hi (c) Calculate the probability that we will obtain a sample mean greater than 19, that is, calculate P> 19. Hint: Find the z value corresponding to 19 by using Hz and 5 because we wish to calculate a probability about (Use the rounded standard error to compute the rounded Z-score used to find the probability. Round your answer to 4 decimal places. Round z-scores to 2 decimal places.) > 19) (d) Calculate the probability that we will obtain a sample mean less than 17.564 that is, calculate 17.564) (Use the rounded standard error to compute the rounded Z-score used to find the probability. Round your answer to 4 decimal places. Round z-scores to 2 decimal places) P

Explanation / Answer

2) a) the distribution is normal as the number of sample = 72 which is larger then 30. hence due to large size

b) mean = 18 given

standarddeviation = 9/sqrt(72) = 1.07

c) we need to find p(x>19) =

For x = 19, z = (19 - 18) / 1.07 = 0.93

Hence P(x > 19) = P(z > 0.93) = [total area] - [area to the left of 0.93]

1 - [area to the left of 0.93]

now from the z table we will take the value of z score = 0.93

    = 1 - 0.8238 = 0.1762

d) p(x<17.564) =

For x = 17.564, the z-value z = (17.564 - 18) / 1.07 = -0.40

Hence P(x < 17.564) = P(z < -0.4), now from the z table we will take the value of z score = -0.4

And that value will be the probability required.

= [area to the left of -0.4] = 0.3446

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.