Question

NO LINKS!!

Please help me with these

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Answer 1

`\textsf{If }\: X \sim\textsf{N}(\mu,\sigma^2)\:\textsf{ then }\: (X-\mu)/(\sigma)=Z, \quad \textsf{where }\: Z \sim \textsf{N}(0,1)`

Math

`\textsf{If }\: X \sim\textsf{N}(71,6.5^2)\:\textsf{ then }\: (X-71)/(6.5)=Z, \quad \textsf{where }\: Z \sim \textsf{N}(0,1)`

Science

`\textsf{If }\: X \sim\textsf{N}(62,8.0^2)\:\textsf{ then }\: (X-62)/(8.0)=Z, \quad \textsf{where }\: Z \sim \textsf{N}(0,1)`

z-score Information

• Positive z-score = data point is above average
• Negative z-score = data point is below average
• z-score close to zero = data point is close to average
• If a data point's z-score is below -3 or above 3 (more than 3 standard deviations from the mean) it can be considered unusual.

Question 3

Math

`X=75 \implies Z=(75-71)/(6.5)\right) \implies Z=0.6154`

Science

`X=71 \implies Z= (71-62)/(8.0) \implies Z=1.125`

The student's math score is below average, whereas their science score is above average. Therefore, the student did better on the science test.

Question 4

Math

`X=91 \implies Z=(91-71)/(6.5) \implies Z=3.0769`

Science

`X=85 \implies Z=(85-62)/(8.0) \implies Z=2.875`

The student's math and science scores are both above average, but the math score is further away from the mean. Therefore, the student did better on the math test.

Question 5

Math

`X=65 \implies Z=(65-71)/(6.5) \implies Z=-0.9231`

Science

`X=54 \implies Z=(54-62)/(8.0) \implies Z=-1`

The student's math and science scores are both below average, but the science score is further away from the mean. Therefore, the student did better on the math test.