Stepwise Descriptive Statistics Learning

People with z-scores above 2.5 on an IQ test are sometimes classified as geniuses. If IQ scores have a mean of 100 and a standard deviation of 16 points, what IQ score do you need to be consideblack a genius?

A set of data has a normal distribution with a mean of 180 and a standard deviation of 20. What percent of the data is in the interval 140 - 220?

What is the z-score of sample X, if ${\displaystyle n=100,\mu =61,St.Dev.=43,\text{and}E\left[X\right]=98}$?

Which of the following statements is true?
a. Systematic reviews and meta-analyses are the same.
b. Census studies determine casual relationships.
c. Qualitative and quantitative data collection methods produce the same level of evidence.
d. none of the above

How do you find z-score given the data:-6, -9, -6, -4, 10? 1. 0.2321 2. -1.737 3. 0.8685 4. 0.9355 5. 6.500?

If $X$ is $N(\mathrm{\mu <!--\; \mu \; -->};{\mathrm{\sigma <!--\; \sigma \; -->}}^2)$, then show that $Z=\frac{(X-<!--\; -\; -->\mathrm{\mu <!--\; \mu \; -->})}{\mathrm{\sigma <!--\; \sigma \; -->}}$ is a standard normal random variable; that is, $N(0;1)$

Here is how far I have gotten:
$P(Z\le <!--\; \le \; -->z)=P(X\le <!--\; \le \; -->z\mathrm{\sigma <!--\; \sigma \; -->}+\mathrm{\mu <!--\; \mu \; -->})={\int <!--\; \int \; -->}_{\frac{x-<!--\; -\; -->\mathrm{\mu <!--\; \mu \; -->}}{\mathrm{\sigma <!--\; \sigma \; -->}}}^z\frac{e^{\frac{-<!--\; -\; -->y^2}{2}}}{\sqrt{2\mathrm{\pi <!--\; \pi \; -->}}}\mathrm{d}y.$
I used $x=y\mathrm{\sigma <!--\; \sigma \; -->}+\mathrm{\mu <!--\; \mu \; -->}$ as my change of variable.
1.) Is my result correct so far?
2.) And what is my next step? This integral is out of my scope.

If Z denotes the standard normal random variable , then
$P(-<!--\; -\; -->.58<Z<.23)$?

What is the z-score of sample X, if ${\displaystyle n=144,\mu =61,St.Dev.=12,\text{and}E\left[X\right]=62}$

Explain what Cohen's d and $r^2$ measure when calculated for a t test

Linear functions versus Logarithmic and Exponential functions
If a function is linear, I know that this should be true:
$f(x_2)-<!--\; -\; -->f(x_1)=f(\stackrel{¯<!--\; ¯\; -->}{x})$
Where $\stackrel{¯<!--\; ¯\; -->}{x}$ is the point exactly in between $x_1$ and $x_2$. Now, I know from looking at their graphs that the same shouldn't be true for logarithmic and exponential functions. That is, for logarithmic functions:
$f(x_2)-<!--\; -\; -->f(x_1)<f(\stackrel{¯<!--\; ¯\; -->}{x})$
And for exponential functions:
$f(x_2)-<!--\; -\; -->f(x_1)>f(\stackrel{¯<!--\; ¯\; -->}{x})$
I'm not a mathematician by formation, but I feel like it should be possible to prove this without having to look at their graph. Does anyone know how to do this?

what is meta analysis and how do a meta analysis in Gene expression

Frequently, a hypothesis is supported by some studies but not by others. When faced with this situation, many researchers rely on a statistical technique known as _____.

meta-analysis
study enumeration
discriminant analysis
replication

What is the range of 2,1,7,3,5,2,9,7,10,4,2,10?

Fine the area , to the nearest thousandth, of the standard distribution between the given z-scores. Z equals 0 and z equals 1.5

How do you find the domain and range of $g(x)=5e^x$?

How do you find the z-score that has 93.82% of the distribution's area to its left?

What is the range of $f(x)=-<!--\; -\; -->3^x+4$?

When using the cumulative normal distribution table, the area under the curve given is the area to the _____ of that particular z-score.
One method of finding the area to the right of a particular z-score, is to use the following: 1 - area to the _____
To find the area _____ two z-scores, we look up the area to the _____ of each value and subtract the smaller area from the larger area.
To find the area _____ of two z-scores, we add together the area to the _____ of the smaller z-score with the area to the _____ of the larger z-score.

What is the z-score of sample X, if ${\displaystyle n=64,\mu =56,SD=20,\text{and}E\left[X\right]=320}$?

Researchers are planning a study to estimate the impact on crop yield when no-till is used in combination with residue retention and crop rotation. Based on data from a meta-analysis of 610 small farms, the researchers estimate there is a 2.5% decline in crop yield when no-till is used with residue retention and crop rotation. Suppose the researchers want to produce a 95% confidence interval with a margin of error of no more than 1.0%. Determine the minimum sample size requiblack for this study.
The sample size needed to create a confidence interval estimate depends on the margin of error, the initial estimated proportion, and the confidence level. Be sure to use proportions rather than percentages. Round your final answer up to the nearest whole number.
n = $\mathrm{◻<!--\; ◻\; -->}$ field comparisons

Suppose that administrators of a large school district wish to estimate the proportion of children in the district enrolling in kindergarten who attended preschool. They took a simple random sample of children in the district who are enrolling in kindergarten. Out of 60 children sampled, 42 had attended preschool.
Construct a large-sample 99% z-confidence interval for p, the proportion of all children enrolled in kindergarten who attended preschool. Give the limits of the confidence interval as decimals, precise to at least three decimal places.
lower limit :
upper limit :

Construct a plus four 99% z-confidence interval for p. Give the limits of the confidence interval as decimals, precise to at least three decimal places.
lower limit :
upper limit :