Finding lower and upper limits based on a known distribution

Please show me how to do these problems correctly.

A nationwide test taken by high school sophomores and juniors has three sections, each scored on a scale of 20 to 80. In a recent year, the national mean score for the writing section was 49.6, with a standard deviation of 10.9. Based on this information, complete the following statements about the distribution of the scores on the writing section for the recent year.

1. According to Chebyshev's theorem, at least what percent of the scores lie between 27.8 and 71.4?
2. According to Chebyshev's theorem, at least 89% of the scores lie between _ and _ (round your answer to 1 decimal place.)
3. Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the scores lie between _ and _
4. Suppose that the distribution is bell-shaped. According to the empirical rule approximately what percent of the scores lie between 27.8 and 71.4?

... Z scores and percentiles based on a ... Empirical Theoretical Lower Limit Upper limit Lower Limit Upper limit 68% 118 142 118.072 ... 1. Find the probability that a ...

... Step 2: Find the 95% confidence interval. ... Significance level=α= No of tails= 2 This is 2 tailed because we are calculating upper and lower confidence level. ...

... 2022, 2319, 2106, 2410, 2034 Based on this sample, find a 99 ... What is the lower limit of the confidence interval ... What is the upper limit of the confidence interval ...

... What do conclude from the results found in questions 26 and 27? ... 2.576*sqrt(0.91*( 1-0.91)/1335)=0.020 Lower limit: 0.91-0.020=0.890 Upper limit: 0.91+0.020 ...

... manager-controlled companies in New Zealand is found to give ... 33 margin of error 6.547916 Mean 82.6 Upper limit 89.14792 Lower limit 76.05208 therefore ...

...Upper confidence limit= p+z*sp= 24.29% =22.9%+1.96*.71% Lower confidence limit... A random selection of 1,600 people found that 900 support a certain lawyer ...

... b). Find the probability that the return for common stocks will be less than ... Confidence Interval Interval Lower Limit 0.82 Interval Upper Limit 9.46 Width ...