point estimate A sample of 81 observations is taken from a normal population with a standard deviation of 5. The sample mean is 40. Determine the 95% confidence interval for the population mean

The 95 percent Confidence Interval is for the population is (38.911 , 41.089)

Step-by-step explanation:

To solve the above question, we would be making use of the confidence interval formula:

Confidence Interval = Mean ± z score × σ/√n

In the above question,

Mean = 40

σ = Standard deviation = 5

n = number of samples = 81

Confidence Interval = 95%

The z score for a 95% confidence interval = 1.96

Therefore, the confidence interval =

= 40 ± 1.96 (5/√81)

= 40 ± 1.96(5/9)

= 40 ± 1.0888888889

Confidence Interval

a)40 + 1.0888888889

= 41.0888888889

Approximately = 41.089

b ) 40 - 1.0888888889

= 38.911111111

Approximately = 38.911

Therefore, the 95 percent Confidence Interval is for the population is (38.911 , 41.089)

step-by-step explanation:

d

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.