1. Find each of the requested values for a population with a mean of ?=40, and a standard deviation of ?=8 A. What is the z-score corresponding to X=52? B. What is the X value corresponding to z=−0.50? C. If all of the scores in the population are transformed into z-scores, what will be the values for the mean and standard deviation for the complete set of z-scores? D. What is the z-score corresponding to a sample mean of M=42 for a sample of n=4 scores? E. What is the z-scores corresponding to a sample mean of M=42 for a sample of n=6 scores? 2. True or false: a. All normal distributions are symmetrical b. All normal distributions have a mean of 1.0 c. All normal distributions have a standard deviation of 1.0 d. The total area under the curve of all normal distributions is equal to 1 3. Interpret the location, direction, and distance (near or far) of the following zscores: a.−2.00b.1.25c.3.50d.−0.34 4. You are part of a trivia team and have tracked your team’s performance since you started playing, so you know that your scores are normally distributed with μ=78 and σ=12. Recently, a new person joined the team, and you think the scores have gotten better. Use hypothesis testing to see if the average score has improved based on the following 8 weeks’ worth of score data: 82,74,62,68,79,94,90,81,80. 5. You get hired as a server at a local restaurant, and the manager tells you that servers’ tips are $42 on average but vary about $12(μ=42,σ=12). You decide to track your tips to see if you make a different amount, but because this is your first job as a server, you don’t know if you will make more or less in tips. After working 16 shifts, you find that your average nightly amount is $44.50 from tips. Test for a difference between this value and the population mean at the α=0.05 level of significance.

Question

l1koV · Accepted Answer

(A) Obtain the z-score corresponding to X=52. The z-score corresponding to X=52 is obtained below as follows, From the information given that, Let X denotes the random variable with the population mean 40 and the standard deviation of 8 Thatis, μ=40,σ=8 The required value is, z=X−μσ =52−408=128 =1.50 Thus, the value of the z-score corresponding to X=52 is 1.50. (B) Obtain the X value corresponding to z=–0.50. The X value corresponding to z=–0.50 is obtained below as follows: The required value is, z=X−μσ −0.50=X−408 −0.50×8.0=X−40 −4.00=X−40 X=40−4 =36 Thus, the X value corresponding to z=–0.50 is 36 It is clear that standard normal distribution represents a nommal curve with mean 0 and standard deviation 1 if the scores in the population are transformed into z-scores with the parameters involved in a nommal distribution are mean (μ) and standard deviation (σ). Determine the value of mean if all of the scores in the population are transformed into z-scores The value of mean if all of the scores in the population are transformed into z-scores is 0. Determine the value of standard deviation if all of the scores in the population are transformed into z-scores. The value of standard deviation if all of the scores in the population are transformed into z-scores is 1.