The weight of adult male grizzly bears living in the wild continental United States is normally distributed with a mean of 500 pounds and a standard deviation of 50 pounds. The weight of adult female grizzly bears is normally distributed with a mean of 300 pounds and a standard deviation of 40 pounds.

(a) What is the probability that a randomly selected female grizzly bear weighs between 275 and 350 pounds? Make sure to find all appropriate z-scores and show your work. When using wolframalpha, describe what you did to get your answers. (2 pts)

(b) Approximately what would the weight of a male grizzly bear be with the same standardized score (z-score) as a female grizzly bear with a weight of 330 pounds? (2 pts)

(c) Is a male grizzly bear weighing 420 pounds unusual? Justify your answer. (1 pt)

2 A poll was conducted in 2019 in which they surveyed people all over the United States and found that 69% of adults in the U.S. believe that global warming is happening. Assume that this is the population proportion of U.S. adults who believe global warming is happening (p= 0.69), and suppose we repeatedly select random samples of size 250, and ask them the same question.

(a) Find the mean, /, and standard error, / of the sampling distribution of sample proportions for the given n and p. (2pts)

(b) Use the Empirical Rule to find the interval centered at p that contains approximately 99.7% of all sample proportions. (1 pt)

(c) Suppose that in a random sample of 250 people, 155 say that global warming is happening. Find the sample proportion and the z-score for this sample proportion. (2 pts)

(d) What is the probability that in a random sample of 250 people, 155 or less will say they think global warming is happening?