In a normally distributed data set with a mean of 24 and a standard deviation of 4.2, what percentage of the data would be between 19.8 and 28.2 and why?
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- Assume that the mathematics scores on the SAT are normally distributed with a mean of 500 and a standard deviation of 100. What percent of students who took the test have a mathematics score between 570 and 640?2. In a departmental examination on statistics, the mean grade was 64 and the standard deviation was 10. If the grades are approximately normally distributed and 40 students got grades between 60 and 70, how many students took the examination?If the weekly grocery expenditure of households in a certain urban market is known to be normally distributed with a mean of $150 and a standard deviation of $30, what proportion of the households spend between $110 and $160 per week on groceries?
- In a population of ages where the mean age is 45 and the standard deviation is 5.25, what are the ages of the youngest 7% and the oldest 12%?The average chef at a restaurant earns $17 an hour with a deviation of $1.75. What are the chances that someone is earning more than $20 an hour?also find test statistics and decision....
- Is it worth pursuing a doctoral degree in education if you already have an undergraduate degree? One way to help make this decision is to look at the mean incomes of these two groups. Suppose that 1212 people with bachelor’s degrees in education were surveyed. Their mean annual salary was $42,000$42,000 with a standard deviation of $9800$9800. Fifteen people with doctoral degrees in education were found to have a mean annual salary of $50,000$50,000 with a standard deviation of $9200$9200. Assume that the population variances are not the same. Construct a 90%90% confidence interval to estimate the true difference between the mean salaries for people with doctoral degrees and undergraduate degrees in education. Let Population 1 be the salaries for people with doctoral degrees and Population 2 be the salaries for people with undergraduate degrees. Round the endpoints of the interval to the nearest whole number, if necessary.Suppose that the heights of 4-year old boys are normally distributed with a mean of 103cm and a standard deviation of 4.05. What height represents the 95th percentile?In a bell-shaped distribution, 95 % of the data falls within 1 standard deviation of the mean.
- The average McDonald's restaurant generates $3 million in sales each year with a standard deviation of 0.4. Russell wants to know if the average sales generated by McDonald's restaurants in Nebraska is different than the worldwide average. He surveys 26 restaurants in Nebraska and finds the following data (in millions of dollars):3.3, 3.2, 3.5, 3.3, 3.3, 3.4, 2.8, 3.5, 3.4, 2.5, 2.5, 3.6, 2.9, 2.9, 2.9, 3.5, 3.4, 2.7, 2.2, 2.5, 3.5, 3.6, 3.5, 3.7, 3.6, 2.8Perform a hypothesis test using a 10% level of significance.Step 1: State the null and alternative hypotheses.H0:(p or u)(<,> #)? Ha: p or u)(<,> #)? (So we will be performing a left or right or 2 tail test.)?Step 2: Assuming the null hypothesis is true, determine the features of the distribution of point estimates using the Central Limit Theorem.By the Central Limit Theorem, we know that the point estimates are normal distributed or t distributed ? with distribution mean ? and distribution…Suppose that the annual household income in a small Midwestern community is normally distributed with a mean of $55,000 and a standard deviation of $4,500. What minimum income does a household need to earn to be in the top 5% of incomes? What maximum income does a household need to earn to be in the bottom 40% of incomes?1. Assume that the time a student stays in school is normally distributed with a mean of 5 hours and a standard deviation of 0.5 hours. Every day, lan stays in school for 5.5 hours. What proportion of students stays less than 5.5 hours?