Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 258 feet and a standard deviation of 58 feet. We randomly sample 49 fly balls. What is the probability that the 49 balls traveled an average of less than 248 feet? (Round answer to four decimal places.)

The average annual rainfall in New York City follows a normal distribution with a mean of 49.9 inches and a standard deviation of 9.5 inches. On what percentage of years can we expect there to be between 40.4 and 59.4 inches of rain in New York City? (A) 100% B) 99.7% C) 95% D) 68%

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 μ=20 inches. However, a survey reported that of a simple random sample of 37 fish caught, the mean length was 17.5 inches, with an estimated standard deviation of 4.3 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than μ=20 inches? Use α=0.05.   What is the value of the test statistic? (Round your answer to two decimal places.)Find the P-value. (Round your answer to four decimal places.)Based on your results, will you reject or fail to reject the null hypothesis? Are the data statistically significant at level αα? A) At the α=0.05α=0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. B) At the α=0.05α=0.05 level, we reject the null hypothesis and conclude the data are statistically significant. C)…

In a large section of a statistics​ class, the points for the final exam are normally​ distributed, with a mean of 74 and a standard deviation of 8. Grades are assigned such that the top​ 10% receive​ A's, the next​ 20% received​ B's, the middle​ 40% receive​ C's, the next​ 20% receive​ D's, and the bottom​ 10% receive​ F's. Find the lowest score on the final exam that would qualify a student for an​ A, a​ B, a​ C, and a D. The lowest score that would qualify a student for an A is nothing. ​(Round up to the nearest integer as​ needed.) The lowest score that would qualify a student for a B is nothing. ​(Round up to the nearest integer as​ needed.) The lowest score that would qualify a student for a C is nothing. ​(Round up to the nearest integer as​ needed.) The lowest score that would qualify a student for a D is nothing. ​(Round up to the nearest integer as​ needed.)