A sample of n = 4 scores is obtained from a population with a mean of 70 and a standard deviation of 8. If the sample mean corresponds to a z score of 2.00, then what is the value of the sample mean?

The value of the sample mean is 78.

Step-by-step explanation:

We are given that a sample of n = 4 scores is obtained from a population with a mean of 70 and a standard deviation of 8.

Also, the sample mean corresponds to a z score of 2.00.

Let = sample mean

The z-score probability distribution for a sample mean is given by;

              Z =  ~ N(0,1)

where, = population mean = 70

             = standard deviation = 8

            n = sample size = 4

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, we are given that the sample mean corresponds to a z score of 2.00 for which we have to find the value of sample mean;

So, z-score formula is given by ;

                  z-score = =

                      2.00 =  

                      2.00 =  

                      = 70 + 8 = 78

Therefore, the value of the sample mean is 78.

the first dot plot best represents the data

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step-by-step explanation:

hans did not square the 40-unit side; he merely multiplied it by 2.   incorrect.