The distribution of course grades in a very large class is (approximately) Normal with mean 48 and standard deviation 14. The minimum possible grade is 0 and the maximum possible grade is 120. A grade of 60 or more is required to pass the course. The course instructor is considering the possibility of a "bell curve" that will increase the mean grade to 77 and decrease the standard deviation to 6. Suppose the instructor will toss a fair or balanced coin to decide what to do and will use the bell curve only if the coin comes up heads. What is the probability that the student at the 50-th percentile will pass the course?

A particular fruit's weights are normally distributed, with a mean of 696 grams and a standard deviation of 25 grams. If you pick 26 fruits at random, then 4% of the time, their mean weight will be greater than how many grams? Give your answer to the nearest gram.

A particular fruit's weights are normally distributed, with a mean of 613 grams and a standard deviation of 19 grams.If you pick 20 fruits at random, then 11% of the time, their mean weight will be greater than how many grams?Give your answer to the nearest gram.

Assume that final exam scores in a given course are approximately normally distributed with a mean of 75 and a standard deviation of 10 points. In a class of 200 students, how many would you expect to fail the exam (i.e., score less than 60) (note: scores can only be approximately normally distributed, because the minimum score is 0, but this should not alter the answer, given how large the mean is relative to the standard deviation).

Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is ? = 19 inches. However, a survey reported that of a random sample of 51 fish caught, the mean length was x = 18.6 inches, with estimated standard deviation s = 3.1 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than ? = 19 inches? Use ? = 0.05.   a) Estimate the P-value. select one:P-value > 0.0100.0010 < P-value < 0.010 0.250 < P-value < 0.00100.125 < P-value < 0.250P-value < 0.125 b) Sketch the sampling distribution and show the area corresponding to the P-value. c) will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.05 level, we reject the null hypothesis and…

A particular fruit's weights are normally distributed, with a mean of 317 grams and a standard deviation of 29 grams. If you pick 25 fruits at random, then 5% of the time, their mean weight will be greater than how many grams? Give your answer to the nearest gram.

A particular fruit's weights are normally distributed, with a mean of 689 grams and a standard deviation of 13 grams.If you pick 10 fruits at random, then 4% of the time, their mean weight will be greater than how many grams?Give your answer to the nearest gram.

Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is ? = 19 inches. However, a survey reported that of a random sample of 51 fish caught, the mean length was x = 18.6 inches, with estimated standard deviation s = 3.5 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than ? = 19 inches? Use ? = 0.05. (a)What is the level of significance? =__   State the null and alternate hypotheses. A-H0: ? = 19 in; H1: ? ≠ 19 in B-H0: ? < 19 in; H1: ? = 19 in  C-H0: ? = 19 in; H1: ? < 19 in D-H0: ? = 19 in; H1: ? > 19 in E-H0: ? > 19 in; H1: ? = 19 in (b)What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. A-The Student's t, since the sample size is large and ? is known. B-The standard normal, since the sample size is large and ? is known. C-The…

Jeff is doing an experiment involving mice. The mice weights have mean weight 3.74 ounces and standard deviation 0.026 ounces. Jeff selects 100 mice independently and calculates the sample mean, x̄, of their weights. What is the standard deviation of x̄?

A particular fruit's weights are normally distributed, with a mean of 580 grams and a standard deviation of 30 grams.If you pick 100 fruits at random, then 20% of the time, their mean weight will be greater than how many grams?Enter your answer to the nearest gram.