for a set of data with a mean of 32 and a standard deviation of 4, chebyshevs thm. states that at least 75%…

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

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

Answer

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