Consider this normal distribution graph and the information below for the next two questions: uaverage, sigma standard deviation. Question 8 Percents are probabilities of being within the indicated segments of the X axis. 0.13% 2.14% 13.59% 34.13% 34.13% 13.59% 2.14% 0.13% For example, there is a 34.13% probability of being between u and u + sigma μ-4σ μ-30 μ-20 н-о H H+o μ+20 μ+3σμ+40 You have analyzed 30 years of historical, annual returns of Vanguard's VIOO ETF. VIOO aims to follow the performance of the S&P 600 Small-Cap stock index. (The S&P 500 is a large-cap index). You found the average return = 10% and the standard deviation of returns 20%. You plan to model future VIOO returns (for better or worse) as normally distributed, based on your historical analysis. Question 91 What is the probability that, in any given future year, the VIOO return will be 30% or better? Round your answer to three decimal places. What is the probability that, in any given future year, the VIOO return will be -30% or worse? Round your answer to three decimal places.

Question 3 The composite scores of individual students on the ACT college entrance examination in 2019 followed a Normal distribution with mean 20.8 and standard deviation 5.8. What is the probability that the mean score of an SRS of 100 students is 22 or higher? O.896 0.0193 O.916 O.084

* 00 T Question 19 A manufacturer knows that their items have a normally distributed lifespan, with a mean of 7.2 years, and standard deviation of 1.4 years. If you randomly purchase one item, what is the probability it will last longer than 4 years? Submit Question MacBook Air 08 F3 F1 F2 F5 DD 23 & 2 %24 % 3. 4. 5. R M S G. B.

Asap A large group of students took a test in Physics and the final grades have a mean of 70 and a standard deviation of 10. If we can approximate the distribution of these grades by a normal distribution, A.  what percent of the students scored higher than 65 but lesser than 90? 47.72% 28.57% 19.15% 66.87% B.  what percent of the students should pass the test (greater than 60)? 84.13% 0.8314 34.13% 0.3143 C.  In a recent study, the Centers for Disease Control and Prevention reported that diastolic blood pressures of adult women in the United States are approximately normally distributed with mean 80.5 and standard deviation 9.9. What proportion of women have blood pressure between 75 and 90? 0.4763 0.1192 0.3486 0.5438