Question

NO LINKS!!Please help me with these​

Answer 1

Answer:

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

Math

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

Science

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

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

$X=75 \implies Z=\dfrac{75-71}{6.5}\right) \implies Z=0.6154$

Science

$X=71 \implies Z= \dfrac{71-62}{8.0} \implies Z=1.125$

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

$X=91 \implies Z=\dfrac{91-71}{6.5} \implies Z=3.0769$

Science

$X=85 \implies Z=\dfrac{85-62}{8.0} \implies Z=2.875$

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

$X=65 \implies Z=\dfrac{65-71}{6.5} \implies Z=-0.9231$

Science

$X=54 \implies Z=\dfrac{54-62}{8.0} \implies Z=-1$

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.