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max2010maxim [7]
3 years ago
13

Penny Weights, use the weights of the post 1983 pennies to construct a 98% confidence interval estimate of the standard deviatio

n of the weights of all post-1983 pennies. S=0.0165 n=37. Find confidence interval. a. 0.01231 < Ï < 0.2111 b. 0.01239 < Ï < 0.02111 c. 0.1391 < Ï < 0.2311 d. 0.001219 < Ï < 0.002111
Mathematics
1 answer:
Ronch [10]3 years ago
7 0

Answer:

c. 0.1391 < Ï < 0.2311

Step-by-step explanation:

The formula for Confidence Interval is given as:

Mean ± z × Standard deviation/√n

Z score for 98% confidence interval = 2.326

Mean = Significance level = 100% - 98%

= 2% = 0.02

Standard deviation = S=0.0165

n= 37

Hence,

Confidence Interval =

0.02 ± 2.326 × 0.0165/√37

0.02 ± 0.0063094687

Confidence Interval

0.02 - 0.0063094687

= 0.1391

0.02 ± 0.0063094687

= 0.2311

Hence, the Confidence Interval = (0.1391, 0.2311)

= c. 0.1391 < Ï < 0.2311

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The z scores are approximately:

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=====================================================

Further Explanation:

We'll need to convert each given score to a corresponding standardized z score.

The formula to use is

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  • x = given grade for each class
  • mu = mean
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Let's find the z score for the Care of Magical Creatures class

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Repeat this process for the Defense Against the Dark Arts score.

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z = 0.583 approximately

And for the Transfiguration class as well

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The negative z score means his grade below the average, whereas earlier the other scores were above the average since he got positive z scores.

Now do the final class (Potions) to get this z score

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This grade is below average as well.

----------------------------

To summarize, we have these z scores

  • Care of Magical Creatures:  z = 0.333
  • Defense Against the Dark Arts:  z = 0.583
  • Transfiguration:  z = -0.263
  • Potions: z = -0.533

Harry did his best in Defense Against the Dark Arts because the z score of 0.583 (approximate) is the largest of the four z scores. On the other hand, his worst grade is in Potions because -0.533 is the lowest z score.

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