You need to ask 1 question at a time, rewording it into 200 characters or less - it helps you to actually think about what is required instead of getting others to do your work for you.
z = (x - µ)/standard deviation
= (52 - 50)/20
= 0.1
(If z is negative it is below the mean.)
64.
1.41
No. Standard deviation is not an absolute value. The standard deviation is often written as a single positive value (magnitude), but it is really a binomial, and it equals both the positive and negative of the given magnitude. For example, if you are told that for a population the SD is 5.0, it really means +5.0 and -5.0 from the population mean. It defines a region within the distribution, starting at the lower magnitude (-5.0) increasing to zero (the mean), and another region starting at zero (the mean) and increasing up to the upper magnitude (+5.0). Both regions together define the (continuous) region of standard deviation from the mean value.
The variance is the square of the standard deviation.This question is equivalent tocan s = s^2The answer is yes, but only in two cases.If the standard deviation is 1 exactly, then so is the variance.If the standard deviation is 0 exactly, then so is the variance.If the standard deviation is anything else, then it is not equal to the variance.You are not likely to find these special cases in practical problems, so from a practical sense, you should think that they are generally not equal.
2.16
The cumulative probability up to the mean plus 1 standard deviation for a Normal distribution - not any distribution - is 84%. The reference is any table (or on-line version) of z-scores for the standard normal distribution.
0.8413
You cannot. There is no information about the distribution, or even what the graph is meant to display!
64.
For a binomial probability distribution, the variance is n*p*q which is 80*.3*.7 = 16.8. The standard deviation is square root of the variance which is 4.099; rounded is 4.1. The mean for a binomial probability distribution is n*p or 80*.3 or 24.
Bob scored 300 or 700.
It equals 14641.
The answer is about 16% Using the z-score formula(z = (x-u)/sd) the z score is 1. This means that we want the percentage above 1 standard deviation. We know from the 68-95-99.7 rule that 68 percent of all the data fall between -1 and 1 standard deviation so there must be about 16% that falls above 1 standard deviation.
6.3
It is the Standard Normal distribution.
The answer depends on what population characteristic A measures: whether it is mean, variance, standard deviation, proportion etc. It also depends on the sampling distribution of A.
1.41