Question

Comsider a population of size N=5,400 with a mean of μ=165 and standard deviation of σ=29. Compute the following z-values for either the population distribution or the sampling distributions of y with given sample size. Round solutions to two decimal places, if necessary. Suppose a random single observations is selected from the population. Calculate the avvalue that corresponds to x=156. Suppose a random single observations is selected from the population. Calculate the a-value that corresponds to x=165. Suppose a random sample of 60 observations is selected from the population. Calculate the z-value that corresponds to x=163. Suppose a random sample of 87 observations is selected from the population. Calculate the s-value that corresponds to x=156.

Answer 1

To calculate the z-values, use the formula: z = (x - μ) / σ. For the given values, the z-values are -0.31, 0, -0.45, and -1.47.

Step-by-step explanation:

To calculate the z-values, we use the formula:

z = (x - μ) / σ

where z is the z-value, x is the given value, μ is the mean, and σ is the standard deviation.

For the given values:

• The z-value for x = 156 is: (156 - 165) / 29 = -0.31
• The z-value for x = 165 is: (165 - 165) / 29 = 0
• The z-value for x = 163 and sample size = 60 is: (163 - 165) / (29 / √60) = -0.45
• The z-value for x = 156 and sample size = 87 is: (156 - 165) / (29 / √87) = -1.47