Question

Calculate the standard score of the given x value, x=52.6 , where μ=48.9 and σ=48.4 and indicate on the curve where z will be located. round the standard score to two decimal places.

Answer 1

The standard score, also known as the z-score, measures how many standard deviations a particular value is from the mean of a distribution. The z-score for x=52.6 is approximately 0.08, indicating that this value is slightly above the mean of μ=48.9.

Step-by-step explanation:

The standard score, also known as z-score, measures how many standard deviations a particular value is from the mean of a distribution. To calculate the z-score for the given x value, x=52.6, you can use the formula:

z = (x - μ) / σ

Plugging in the values for this problem:

z = (52.6 - 48.9) / 48.4 = 0.0769

Rounded to two decimal places, the standard score is approximately 0.08.

The z-score tells you the position of the value on the standard normal distribution curve. Since the z-score is positive, the x value of 52.6 will be located to the right of the mean μ=48.9.