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.