An investment analyst would like to estimate the average amountinvested in a particular mutual fund by institutional investors. Arandom sample of 15 institutional investors' portfolios has beenchosen. The observed sample mean of the amounts invested in themutual fund by these 15 investors is $11.32 million and theobserved sample standard deviation is $4.4 million. Assume the portfolios are distributed normally. Required:
a. Construct a 90% confidence interval for the mean amount invested by all institutional investors in the mutual fund.
b. Determine the required sample size in order to estimate the mean amount invested by all institutional investors in this mutual fund to within $500,000, at the 95% confidence level.

If cos(2x) = tan^2(y), show that cos(2y) = tan^2(x).

Find each value of the five-number summary for this set of data. [note: type your answers as numbers. do not round.] 46, 19, 38, 27, 12, 38, 51 minimum maximum median upper quartile lower quartile

(50 ) mrs. julien’s and mrs. castillejo’s classes are selling cookie dough for a school fundraiser. customers can buy packages of macadamia nut chip cookie dough and packages of triple chocolate cookie dough. mrs. julien’s class sold 25 packages of macadamia nut chip cookie dough and 30 packages of triple chocolate cookie dough for a total of $221.25. mrs. castillejo’s class sold 5 packages of macadamia nut chip cookie dough and 45 packages of triple chocolate cookie dough for a total of $191.25. (a) write the system of equations that model the problem. be sure to explain which equation represents which situation. (b) find the cost of each type of cookie. show your work. (c) explain which method you used to solve the system and why you chose that method.