Compute the population mean margin of error for a 90% confidence interval when sigma is 7 and the sample size?

Question

is 36

The area under a normal curve with mu = 35 and sigma = 7 is

f John gets an 90 on a physics test where the mean is 85 and the standard deviation is 3, where does he stand in relation to his classmates?

he is in the top 5%

he is in the top 10%

he is in the bottom 5%

he is in the bottom 1%

Find P(12 < x < 23) when mu = 19 and sigma = 6. Write your steps in probability notation

In a normal distribution with mu = 34 and sigma = 5 what number corresponds to z = -4?

Let’s assume you have taken 1000 samples of size 64 each from a normally distributed population. Calculate the standard deviation of the sample means if the population’s variance is 49.

Interpret a 93% confidence interval of (7.46, 12.84) for a population mean.

The area to the left of "z" is .5438. What z score corresponds to this area?

What is the critical z-value that corresponds to a confidence level of 86%?

Answer 1

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Compute the population mean margin of error for a 90% confidence interval when sigma is 7 and the sample size?

is 36

Margin of error = m

Confidence level= 90%

standard deviation = 7

sample size = n = 36

first, find z* or z star, at 90% confidence level, its 1.645

m = 1.645*7/sqrt(36)

= 1.645*7/6

= 1.919

m = 1.919

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if John gets an 90 on a physics test where the mean is 85 and the standard deviation is 3, where does he stand in relation to his classmates?

he is in the top 5%

he is in the top 10%

he is in the bottom 5%

he is in the bottom 1%

mean = 85

standard deviation = 3

x = 90

find the z score, with the corresponding p value or the probability.

z = ( 90 - 85) / 3 = 1.67

1.67 is only the z score, you need to find the p on the z score table, and its 0.9525 or at 95.3th place from bottom.

his above the 5% top in the class.

Why ? because 1 - 0.9525 = 0.0475 or less than 5%

Therefore, he is in the top 5%

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Find P(12 < x < 23) when mu = 19 and sigma = 6. Write your steps in probability notation

the idea is using z score table, again.

mean = 19

standard deviation = 6

at 12, z = (12 - 19)/ 6 = -1.17 or p = 0.1210

at 23, z = (23-19)/6 = 0.67 or p = 0.7486

in between, 0.7486 - 0.1210 = 0.6276 or 62.76%

Answer: p = 0.6276 or 62.76%

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In a normal distribution with mu = 34 and sigma = 5 what number corresponds to z = -4?

mean = 34

standard deviation = 5

z = -4

find x?

(x - 34) / 5 = -4

the idea is you just solve for x

x - 34 = -20

x = -20 + 34 = 14

x = 14

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Let’s assume you have taken 1000 samples of size 64 each from a normally distributed population. Calculate the standard deviation of the sample means if the population’s variance is 49.

population:

variance = 49

standard deviation = sqrt(s^2) = sqrt(49) = 7

sample:

standard deviation ?

n = 1000

standard deviation of sample=

7/sqrt(1000) =0.2214

s = 0.2214

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Interpret a 93% confidence interval of (7.46, 12.84) for a population mean.

The idea is the true population mean will be 93% confident that be between 7.46 and 12.84 or we are 93% confident that the true mean of the population will be between 7.46 and 12.84.

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The area to the left of "z" is .5438. What z score corresponds to this area?

Use the z score table to find the corresponding, the idea is the probability or the area to the left is 0.5438.

p = 0.5438

z from the table is 0.11

z = 0.11

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What is the critical z-value that corresponds to a confidence level of 86%?

so I dont know the exact value, since my table doesnt expand into the 0.01% and I only have it between 1.645 and 1.960 which is between 80% and 90% confidence interval.

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