The commute times for workers in a city are normally distributed with an unknown population mean and standard deviation. If a random sample of 20 workers is taken and results in a sample mean of 21 minutes and sample standard deviation of 6 minutes, find a 95% confidence interval estimate for the population mean using the Student's t-distribution.

The 95% confidence interval estimate for the population mean using the Student's t-distribution is between 10.626 minutes and 31.374 minutes.

Step-by-step explanation:

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 20 - 1 = 19

Now, we have to find a value of T, which is found looking at the t table, with 19 degrees of freedom(y-axis) and a confidence level of 0.99(). So we have T = 1.729

The margin of error is:

M = T*s = 1.729*6 = 10,374.

In which s is the standard deviation of teh sample. So

The lower end of the interval is the sample mean subtracted by M. So it is 21 - 10.374 = 10.626 minutes

The upper end of the interval is the sample mean added to M. So it is 21 + 10.374 = 31.374 minutes.

The 95% confidence interval estimate for the population mean using the Student's t-distribution is between 10.626 minutes and 31.374 minutes.

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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∠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.