Question

12. Using a normal distribution and z score formula answer the following questions: a. Find the Z-score that cuts off the top 35% of the nornval curve b. Find the data value to the nearest whole number that cuts off the bottom 20% of the curve given that the mean is 75 and sample standard deviation is 5. c. Find the z scores that cut off the middle 50% of the normal curve. 13. This question is worth 4 points only. A statistics professor has surveyed 225 NCC students to determine the cost of their textbooks for the semester. He determined that the sample mean was $425 with a population standard deviation of S75 i) ii) iii) Determine the standard error of a 95% confidence interval Determine the 95% confidence interval (round to the nearest whole number) Determine the 99% confidence interval (round to the nearerst whole #)
12-13 show work

Answer 1

We would be looking at the first question all parts here as:

Q12) a) From standard normal tables, we have here:
P(Z < 0.385) = 0.65

Therefore, P(Z < 0.385) = 1 - 0.65 = 0.35

Therefore 0.385 is the required z score here which cuts off the top 35% of the normal curve.

b) From standard normal tables, we have here:
P(Z < -0.842) = 0.2

Therefore the cuttoff value here is computed as:
= Mean -0.842*Std Dev

= 75 -0.842*5

= 70.79

Therefore 70.79 is the required cutoff value here.

c) From standard normal tables, we have here:
P(Z < 0.674) = 0.75

Therefore, due to symmetry, we have here:
P(-0.674 < Z < 0.674) = 0.5

Therefore -0.674, 0.674 are the required z scores here which cut off the middle 50% of the normal curve here.