Five friends go bowling and finish with the following scores. Jim bowls a 129, Bob bowls a 150, Ann bowls a 133, Tom bowls a 162 and Gina bowls a 148. Find Tom's z-score. Treat the data as a population. Don't forget to round to the nearest tenth.

The book says value-mean divided by sd. I have no idea what sd is.

sd=standard deviation

oh thank you.

To find Tom's z-score, we need to first calculate the mean and standard deviation (sd) of the scores.

Step 1: Calculate the mean (average) of the scores.

Mean = (Jim's score + Bob's score + Ann's score + Tom's score + Gina's score) / 5
= (129 + 150 + 133 + 162 + 148) / 5
= 722 / 5
= 144.4

So, the mean score is 144.4.

Step 2: Calculate the standard deviation (sd) of the scores.

To calculate the standard deviation, we need to find the differences between each score and the mean, square these differences, find the average of the squared differences, and then take the square root.

Calculate the squared differences for each score:
(Jim's score - Mean)^2 = (129 - 144.4)^2 = (-15.4)^2 = 237.16
(Bob's score - Mean)^2 = (150 - 144.4)^2 = 5.6^2 = 31.36
(Ann's score - Mean)^2 = (133 - 144.4)^2 = (-11.4)^2 = 129.96
(Tom's score - Mean)^2 = (162 - 144.4)^2 = 17.6^2 = 309.76
(Gina's score - Mean)^2 = (148 - 144.4)^2 = 3.6^2 = 12.96

Calculate the sum of squared differences:
Sum of squared differences = 237.16 + 31.36 + 129.96 + 309.76 + 12.96
= 721.2

Calculate the average of squared differences (variance):
Variance = Sum of squared differences / Number of scores
= 721.2 / 5
= 144.24

Calculate the standard deviation by taking the square root of the variance:
Standard deviation = √Varience
= √144.24
≈ 12.01

So, the standard deviation is approximately 12.01.

Step 3: Calculate Tom's z-score.

Tom's z-score = (Tom's score - Mean) / Standard deviation
= (162 - 144.4) / 12.01
= 17.6 / 12.01
≈ 1.47

Therefore, Tom's z-score is approximately 1.47 when treating the scores as a population.