# Round each z-score to the nearest hundredth. A data set has a mean of x = 6.8 and a standard deviation of 2.5. Find the z-score. x=7.2

Question
Random variables
Round each z-score to the nearest hundredth.
A data set has a mean of
$$\displaystyle{x}={6.8}$$
and a standard deviation of 2.5. Find the z-score.
$$\displaystyle{x}={7.2}$$

2021-02-26
Obtain the Z-score for the random variable X value equals 7.2.
The Z-score for the random variable X value equals 7.2 is obtained below as follows:
Let X denote the random variable with the population mean 7.2 and the standard deviation of 2.5.
The required value is,
$$\displaystyle{Z}={\frac{{{X}-\mu}}{{\sigma}}}$$
$$\displaystyle={\frac{{{7.2}-{6.8}}}{{{2.5}}}}$$
$$\displaystyle={\frac{{{0.4}}}{{{2.5}}}}=-{0.16}$$
The Z-score for the random variable X value equals 7.2 is 0.16.

### Relevant Questions

Round each z-score to the nearest hundredth.
A data set has a mean of
$$\displaystyle{x}={6.8}$$
and a standard deviation of 2.5. Find the z-score.
$$\displaystyle{x}={5.0}$$
Round each z-score to the nearest hundredth.
A data set has a mean of
$$\displaystyle{x}={6.8}$$
and a standard deviation of 2.5. Find the z-score.
$$\displaystyle{x}={9.0}$$
Round each z-score to the nearest hundredth.
A data set has a mean of
$$\displaystyle{x}={6.8}$$
and a standard deviation of 2.5. Find the z-score.
$$\displaystyle{x}={6.2}$$
Let $$X_{1}, X_{2},...,X_{n}$$ be n independent random variables each with mean 100 and standard deviation 30. Let X be the sum of these random variables.
Find n such that $$Pr(X>2000)\geq 0.95$$.
Random variables $$X_{1},X_{2},...,X_{n}$$ are independent and identically distributed. 0 is a parameter of their distribution.
If $$X_{1}, X_{2},...,X_{n}$$ are Normally distributed with unknown mean 0 and standard deviation 1, then $$\overline{X} \sim N(\frac{0,1}{n})$$. Use this result to obtain a pivotal function of X and 0.
Random variables Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: X+Y
$$\displaystyle{P}{\left({71.4}{<}{x}{<}{78}\right)}={P}{\left({<}{z}{<}\right)}=$$?
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: $$a. -2.00 b. 1.25 c. 3.50 d. -0.34$$ 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 $$12 (\mu = 42, \sigma = 12)$$. 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 $$\alpha = 0.05$$ level of significance.