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.

We have evidence to support the claim.

Assume that the random variable X is normally distributed, with mean

In a recent survey, 65% of park visitors supported adding more hiking trails in the local nature reserve. If 20 visitors are selected at random, what is the mean number who would support adding more trails?

A factory produces light bulbs, and their quality control department claims that the average lifespan of their bulbs is at least 1,000 hours. You are tasked with checking if the average lifespan is less than 1,000 hours. Is this a left-tailed, right-tailed, or two-tailed test?