The chartered financial analyst (cfa) designation is fast becoming a requirement for serious investment professionals. although it requires a successful completion of three levels of grueling exams, it also entails promising careers with lucrative salaries. a student of finance is curious about the average salary of a cfa charterholder. he takes a random sample of 36 recent charterholders and computes a mean salary of $158,000 with a standard deviation of $36,000. use this sample information to determine the 95% confidence interval for the average salary of a cfa charterholder.

(145820, 170180)

Step-by-step explanation:

Formula for confidence interval for population mean ( when population standard deviation is unknown ) :

, where n= sample size

= sample mean

s= sample standard deviation

= two-tailed t-value for significance level of ().

We assume that  the salary of CFA charterholders is normally distributed .

Let x represents the salary of CFA charterholders .

As per given , we have

n=  36

Degree of freedom : df = 35    [ df= n-1]

s=  $36,000

Significance level :

Using t-distribution table ,

95% confidence interval for the average salary of a CFA charterholders :-

Hence, the 95% confidence interval for the average salary of a CFA charterholder : (145820, 170180)

< 4, -5>

step-by-step explanation:

starting from g. we move 4 right and then 5 down to get to h. that means the vector is < 4, -5>

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)