Question

for a set of data with a mean of 32 and a standard deviation of 4, chebyshevs thm. states that at least 75% of the values will fall between ______ and ______. 30 and 34 20 and 44 24 and 40 28 and 36 question 20 (3 points) a student scored 73 points on a test where the mean score was 82 and the standard deviation was 6. find their z - score (i.e. how many standard deviations they are from the mean). 1.04 - 1.5 1.5 - 1.04

Explanation:

Step1: Apply Chebyshev's Theorem for first - part

Chebyshev's Theorem for at least 75% of data gives \(k = 2\) (since \(1-\frac{1}{k^{2}}=0.75\), solving for \(k\) gives \(k = 2\)). The lower bound is \(\mu - k\sigma\) and the upper bound is \(\mu + k\sigma\), where \(\mu = 32\) and \(\sigma=4\).
Lower bound: \(32-2\times4=32 - 8 = 24\)
Upper bound: \(32 + 2\times4=32+8 = 40\)

Step2: Calculate z - score for second - part

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x = 73\), \(\mu = 82\) and \(\sigma = 6\).
\(z=\frac{73 - 82}{6}=\frac{-9}{6}=- 1.5\)

Answer:

First question: C. 24 and 40
Second question: B. -1.5