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A simple random sample of 85 is drawn from a normally distributed population, and the mean is found to be 146, with a standard deviation of 34. Which of the following values is outside the 99% confidence interval for the population mean? Use the table below to help you answer the question.

Remember, the margin of error, ME, can be determined using the formula mc026-1.jpg.
a) the value of 135 because it is not greater than 136.5
b) the value of 137 because it is greater than 136.5
c) the value of 138 because it is less than 153.2
d) the value of 154 because it is greater than 153.2

Respuesta :

Answer:

a) the value of 135 because it is not greater than 136.5

Step-by-step explanation:

Given that

n = sample size =85

Mean = 146

std dev =34

Std error of sample = 34/sqrt 85

= 3.6878

99% z critical value = 2.58

Margin of error = ±9.515

Confidence interval lower bound = 146-9.515 = 136.485

                                 Upper bound = 146+9.515 =155.515

Hence we find that 135 is less than lower bound, hence 135 does not lie within 99% confidence interval

a) the value of 135 because it is not greater than 136.5

The only value that is outside the 99% confidence interval for the population mean is; A: 135 because it is not greater than 136.5.

Confidence Interval

We are given;

Sample size; n =85

Mean; x' = 146

Standard deviation; σ =34

Standard error of sample; s = σ/√n = 34/√85 = 3.6878

Confidence Level = 99%

Formula for confidence interval is;

CI = x' ± z(s/√n)

where z is critical value at confidence level

At 99%  confidence level, z = 2.58

Thus;

CI = 146 ± 2.58(3.6878)

Margin of error = 9.515

CI = 146 ± 9.515 = 136.485

CI = (146 - 9.515) and  (146 + 9.515)

CI = 136.485, 155.515

The only value that is outside the 99% confidence interval for the population mean is 135 because it is not greater than 136.5.

Read more about Confidence interval at; https://brainly.com/question/17097944

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