Have we met the normality requirement for this test? 

A manufacturer claims that their machine can produce at least 100 widgets per hour. However, you suspect that the machine produces more than 100 widgets per hour on average. You want to test if the machine’s output is greater than 100 widgets per hour. Is this a left-tailed, right-tailed, or two-tailed test? 

Provide an appropriate response.Find the variance of the binomial distribution for which n = 40 and p = 0.6.

A recent study shows that the average amount of sleep high school students get on a school night is 6.8 hours, with a standard deviation of 1.2 hours. Angelica is a high school student who reported getting 9.1 hours of sleep on a typical school night.  What is Angelica’s z-score? Round your answer to two decimal places.

Determine whether the distribution represents a probability distribution. If not, identify any requirements that are not satisfied. x P(x) 1 .03 2 .61 3 .15 4 .32

Determine whether the distribution represents a probability distribution. If not, identify any requirements that are not satisfied. x P(x) 1 .31 2 .06 3 .77 4 .81

A dentist is evaluating whether a new whitening toothpaste works better than a standard toothpaste. She recruits married couples and randomly assigns one partner in each couple to use the new toothpaste and the other to use the standard toothpaste. After three weeks, she compares the results within each couple. Determine whether the samples are dependent or independent.

Find the variance of the binomial distribution for which n = 70 and p = 0.3.

IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the IQ score that corresponds to a z-score of 1.96.

A sports scientist tests a new warm-up routine to see if it slows down 40-yard sprint times. H₀: The average sprint time with the new routine is equal to 4.5 seconds. H₁: The average sprint time with the new routine is greater than 4.5 seconds. α = 0.01 p-value = 0.04 Fill in the blanks: At the 1% significance level, the scientist should [blank] the null hypothesis. The scientist has evidence that the new routine [conclusion] slows down 40-yard sprint times.