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Solve the z-score with a mean of 49 and the standard deviation of 20.7 for the following: 1) 32 2) 45 3) 66 4) 55

User Adelmar
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Final answer:

The z-scores for the values 32, 45, 66, and 55 using a mean of 49 and a standard deviation of 20.7 are -0.82, -0.19, 0.82, and 0.29 respectively. These scores indicate how far each value is from the mean in terms of standard deviations.

Step-by-step explanation:

The question involves calculating the z-score for different values given a mean and standard deviation. To find the z-score, we use the formula z = (X - μ) / σ, where X is the value in question, μ (mu) is the mean, and σ (sigma) is the standard deviation. We will calculate the z-scores for the values 32, 45, 66, and 55 using a mean of 49 and a standard deviation of 20.7.

For X = 32: z = (32 - 49) / 20.7 = -0.82

For X = 45: z = (45 - 49) / 20.7 = -0.19

For X = 66: z = (66 - 49) / 20.7 = 0.82

For X = 55: z = (55 - 49) / 20.7 = 0.29

A z-score indicates how many standard deviations a value is from the mean. If it's positive, the value is above the mean; if negative, it's below the mean.

User Ubermensch
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