Questions: Calculate the standard score of the given Y-value: Y = 36.5, where μ = 45.5 and σ = 45 and indicate on the curve where z will be located. Round the standard score to two decimal places.

Calculate the standard score of the given Y-value: Y = 36.5, where μ = 45.5 and σ = 45 and indicate on the curve where z will be located. Round the standard score to two decimal places.

Transcript text: Calculate the standard score of the given Y-value: Y = 36.5, where μ = 45.5 and σ = 45 and indicate on the curve where z will be located. Round the standard score to two decimal places.

Solution

Solution Steps

Step 1: Find the z-score

We are asked to calculate the standard score (z-score) of X = 36.5 given μ = 45.5 and σ = 45. The formula for calculating the z-score is:

z = (X - μ) / σ

Plugging in the values, we have: z = (36.5 - 45.5) / 45 z = -9 / 45 z = -0.2

Step 2: Round to two decimal places

The z-score calculated in Step 1 is already rounded to two decimal places (-0.20).

Step 3: Locate on the curve

The z-score represents the number of standard deviations a data point is away from the mean. In this case, the z-score is -0.2, which means the data point X = 36.5 is 0.2 standard deviations to the left of the mean (μ = 45.5) on the normal distribution curve.