- Find the area of the shaded region. The graph depicts a standard normal distribution with a mean of 0 and a standard deviation of 1. (4 pts)
- Area: ____________
- Area: _____________
- What is the z-score that corresponds to the area of 0.9429 shaded to the left in the graph below. The graph depicts a standard normal distribution with a mean of 0 and a standard deviation of 1. (2 pts)
z =
The blood pressures of adult woman in the US are normally distributed with a mean of
80.5 mmHG and a standard deviation of 9.9. (4 pts)
A blood pressure greater than 88 mmHG is considered high blood pressure. What is the probability that if I randomly select a US woman that she will have a blood pressure greater than 88?
Is it likely that I select a US woman that she will have high blood pressure (greater than 88?)
Weights of babies less than 2 months old in the US are normally distributed with a mean of 11.5 pounds and standard deviation of 2.7 lbs.
What is the weight that represents the 80th percentile for babies less than 2 months old? (Remember this is the weight that has 80 percent of babies below it and 20% of babies above it). (4 pts)
The College Board reports that the mean mathematics SAT score was 523 and the standard deviation was 82.
A random sample of 55 samples were chosen. What is the probability the mean math score of the 55 samples was less than 500? (4 pts)
Find the critical value, zα/2, that corresponds to an 86% confidence interval. You may want to draw a picture to show your work. (2 pts)
A Consumer Reports survey found that 310 people out of 430 surveyed prefer to purchase books online. Use the steps below to construct a 95% confidence interval to estimate the proportion of all people that prefer to purchase books online. (12 pts)
What is the sample proportion of people that prefer to purchase books online?
Find the critical value 𝑧“ that corresponds to a 95% confidence level. #
Calculate “E”
Construct your confidence interval.
Write a sentence that explains the meaning of the confidence interval.I am 95% confident that…
) A bookstore claims that 75% of their customers prefer to buy books online. Does your confidence interval support the bookstores claim?
Given the information on the sample below, use the steps to construct a 95% confidence interval for the population mean. Assume that the population is normally distributed.
A college gives the same calculus final to all sections of the course. A sample of 35 randomly selected students that took the calculus final was collected after the exam. The mean score of the sample was 78 and the standard deviation of the sample was
11.2. (8 pts)
Find the critical value 𝑡“ that corresponds to a 95% confidence level. #
Calculate “E”
Construct your confidence interval.
Write a sentence that explains the meaning of the confidence intervalI am 95% confident that…
Scores on the math portion of the SAT are normally distributed. A sample of 20 SAT scores had a standard deviation of s = 87. (8 pts)
Find the two critical values 𝜒&’ and 𝜒(’ that correspond to a 98% confidence interval for standard deviation built with the sample above.
Construct a 98% confidence interval for the standard deviation on the math portion of the SAT using the information above.
Write a sentence that explains the meaning of the confidence interval. I am 98% confident that….
d) Someone working for testing company claims that the scoring system for the SAT is designed so that the population standard deviation will be 𝜎 = 100. Does this confidence interval support this claim or contradict this claim?
Metro Transit states that the mean wait time between Greenline Trains during peak hours is 12 minutes. An angry statistics student (who is tired of waiting for the train) claims that the average wait time is more than 12 minutes
The clever student took a sample of 30 wait times between Greenline Trains during peak hours. The mean wait time in her sample was 13.2 minutes with a standard deviation of 2.5 minutes.
Using the sample data and steps below and the 0.05 significance level, test student’s claim that the mean wait time between trains is greater than 12 minutes. (10 pts)
- State the claim, null hypothesis and alternative hypothesis. Claim:
𝐻.:
𝐻0:
Find the t-test statistic.
Find the p-value using stat crunch.
Do you reject the null or fail to reject the null? Explain your answer either using your p-value or t-statistic and critical value.
Interpret the results of your hypothesis test. Specifically, does the sample support the students claim that mean wait time is more than 12 minutes?
National Health Statistics sampled 50 one-year-old babies. The mean weight of the babies in the sample was 25.8 pounds with standard deviation of 5.3 pounds.
A leading pediatrician claims that mean weight of one-year old babies is equal to 25 pounds.
Using the sample data and steps below and the 0.05 significance level, test the claim that the average weight of one-year-old babies is equal to 25 pounds. (10 pts)
State the claim, null hypothesis and alternative hypothesis.
- Claim:
𝐻.:
𝐻0:
Find the t-test statistic.
Find the p-value using stat crunch.
Do you reject the null or fail to reject the null?
Interpret the results of your hypothesis test. Specifically does our sample provide evidence against the pediatricians claim that the average weight is equal to 25 pounds, or is it possible that ave
