You observe a portfolio for five years and determine that its average annual return is 13% and the standard deviation of its returns is 21%. Can you be 95% confident that this portfolio will not lose more than 30% of its value next year

There is a 95% probability that the portfolio would not loose more than 30% of its value.

Step-by-step explanation:

The confidence interval for proportions (p) is:

The information provided is:

For 95% confidence level the critical value of z is:

The 95% confidence interval for average annual return is:

The lower limit of the 95% confidence interval is -28%.

This implies that the portfolio would not loose more than 28% of its value.

Thus, there is a 95% probability that the portfolio would not loose more than 30% of its value.

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40

m

step-by-step explanation: