Answer :
Answer:
[tex]Z = -1.63[/tex]
Step-by-step explanation:
The z-score measures how many standard deviation a score X is above or below the mean.
it is given by the following formula:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
In which
[tex]\mu[/tex] is the mean, [tex]\sigma[/tex] is the standard deviation
In this problem, we have that:
Mean weight of all students in a class is 165 pounds, so [tex]\mu = 165[/tex]
Variance of 234.09 square pounds. The standard deviation is the square root of the variance. So [tex]\sigma = \sqrt{234.09} = 15.3[/tex]
What is the z-value associated with a student whose weight is 140 pounds?
Z when X = 140. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{140 - 165}{15.3}[/tex]
[tex]Z = -1.63[/tex]
Final answer:
To find the z-value associated with a student whose weight is 140 pounds, use the formula for calculating z-score. Substitute the values of mean, standard deviation, and the student's weight into the formula.
Explanation:
To find the z-value associated with a student whose weight is 140 pounds, we need to use the formula for calculating z-score:
z = (x - μ) / σ
- Step 1: Calculate the standard deviation by taking the square root of the variance. In this case, the standard deviation is √234.09.
- Step 2: Calculate the z-score using the given formula by substituting the values of x (140 pounds), μ (mean weight of the class - 165 pounds), and σ (standard deviation).
- Step 3: Solve the equation to find the z-score.
The z-value associated with a student whose weight is 140 pounds can be calculated using the given formula and the information provided.
Learn more about z-value calculation here:
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