FizeauV

2020-10-23

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 $\mu =78$ and $\sigma =12$. 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 $12\left(\mu =42,\sigma =12\right)$. 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 $\alpha =0.05$ level of significance.

l1koV

Expert

(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, $\mu =40,\sigma =8$ The required value is, $z=\frac{X-\mu }{\sigma }$
$=\frac{52-40}{8}=\frac{12}{8}$
$=1.50$ Thus, the value of the z-score corresponding to (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, $z=X-\frac{\mu }{\sigma }$
$-0.50=\frac{X-40}{8}$
$-0.50×8.0=X-40$
$-4.00=X-40$
$X=40-4$
$=36$ Thus, the X value corresponding to 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 $\left(\mu \right)$ and standard deviation $\left(\sigma \right)$. 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.

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