3) The classic 1Q test scores form a bell-shaped distribution with a mean of 100

Question

3) The classic 1Q test scores form a bell-shaped distribution with a mean of 100 points and a standard deviation of 15 points. Use the Empirical Rule to answer the following questions: a) Approximately what proportion of test-takers get a score under 70? b) .. between 85 and 130? c) .greater than 130? d) .. between 55 and 130? e)... no greater than 115? no more than 145? 8) .. below 100? formed a bell-shaped distribution, you could not use the Empirical Rule. You 4) If I didn't tell you the IQ scores could only use Chebyshev's Theorem. a) % of test-takers will get between 70 and 130 points. b) % will bet between 55 and 145 points. 5) Marcia scored a 76 on her Biology exam. The mean score was a 70 with a standard deviation of 8 points. She scored 4,625 points on a computer game that has a mean of 4000 points with a standard deviation of 950 points. a) Did Marcia do relatively better on the exam or the game? b) Jan's z-score on the Biology test was a -0.70. What was his gradei? c) Cindy's -score for the computer game was a -2.10. How many points did she score? 6) Using the Coefficient of Variation, which was relatively more variable: The afore-mentioned Biology exam or the computer game?

Explanation / Answer

3) It's a bell shaped curve with mu=mean = 100 and sd =15

a)To find a score under 70 We need to find the z value at X'=70

So using the normal distribution formula for z

Z = (X'-mu)/sd = (70-100)/(15) = -2

And looking at the z table for z=-2 we get p value = 0.02275013

So the answer is 0.02275013 or 2.275% of the test takers score under 70

b) Same process for 85 to 130

We get P(Z> (85-100)/15) to P(Z<(130-100)/15)

So., P(Z>-1) to P(Z<2) and by looking at the z table we get area of curve from z>-1 to z<2 as 0.8185946

c) Same process for greater than 130

P(Z> (130-100)/15) = P(Z>2) = 0.02275013

d)

Same process for 55 to 130

We get P(Z> (55-100)/15) to P(Z<(130-100)/15)

So., P(Z>-3) to P(Z<2) and by looking at the z table we get area of curve from z>-3 to z<2 as 0.9759

As per the Chegg policy & time crunch we are supposed to answer first 4sub parts of the 1st question and so here I have answerd all the required ones. If you need the ans for the rest kindly post the rest seperately. Hope you understand.

Hope the above answer has helped you in understanding the proble. Please upvote the ans if it has really helped you. Good Luck!!

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