consider a population with a mena =51.6 and a sd=5.9 (A) calculate the z score for x= 50.5 from a sample of size 47. (b) could this z score be used in calculating probabilities using table 3 in appendix b in text book ahy or ahy not
It would help if you proofread your questions before you posted them.
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score. Multiply by 47.
Is this your "table 3 in appendix b"?
Twelve different video games showing substance use were observed and the duration times of game play ( in seconds) are listed below. The design of the study justifies the assumption that the sample can be treated as a simple random sample. use the data to construct a 95% confidence interval estimate of mean duration of game play.
4061,3886,3865,4023,4309,4821,4645,4021,5024,4812,4331,4325
To calculate the z-score for a given data point, you need to subtract the mean from the data point and then divide it by the standard deviation. Here's how you can calculate the z-score for x = 50.5 from a sample of size 47:
(a) Calculate the z-score:
Step 1: Subtract the mean from the data point: x - mean = 50.5 - 51.6 = -1.1
Step 2: Divide the result by the standard deviation: z = -1.1 / 5.9 ≈ -0.1864
So, the z-score for x = 50.5 is approximately -0.1864.
(b) To determine whether this z-score can be used in calculating probabilities using Table 3 in Appendix B of a textbook, you need to check if the table provides the z-scores for the desired level of precision. In most standardized normal distribution tables, values are rounded to two decimal places.
In this case, the z-score is -0.1864, which contains more decimal places than what the table provides. Therefore, you will need to either approximate the z-score or use a statistical calculator or software that can calculate the probability more accurately.
Note: Advanced statistical software and calculators can provide more precise probabilities by considering values beyond two decimal places, thus eliminating the need for approximations.