A survey found that women's heights are normally distributed with mean 63.3 in. and standard deviation 3.9 in. The survey also found that men's heights are normally distributed with mean 67.4 in. and standard deviation 3.1 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 56 in. and a maximum of 62 in. Complete parts (a) and (b) below. a. Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as characters at the amusement park? The percentage of men who meet the height requirement is 4.08 %. (Round to two decimal places as needed.) Since most men do not meet the height requirement, it is likely that most of the characters are women. b. If the height requirements are changed to exclude only the tallest 50% of men and the shortest 5% of men, what are the new height requirements? The new height requirements are a mnimum of in. and a maximum of in. (Round to one decimal place as needed.)

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer. Suppose that at five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below. Wilderness District 1 2 3 4 January April 130 127 122 64 78 105 97 108 88 61 Does this information indicate that the peak wind gusts are higher in January than in April? Use a = 0.01. Solve the problem using the critical region method of testing. (Let d = January - April. Round your answers to three decimal places.) test statistic = critical value = Interpret your conclusion in the context of the application. O Reject the null hypothesis, there is insufficient evidence to claim average peak…

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.At five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below. Weather Station 1 2 3 4 5 January 137 124 128 64 78 April 104 115 102 88 61 Does this information indicate that the peak wind gusts are higher in January than in April? Use ? = 0.01. (Let d = January − April.) (a) What is the level of significance? What is the value of the sample test statistic?

For a data set of the pulse rates for a sample of adult​ females, the lowest pulse rate is 38beats per​ minute, the mean of the listed pulse rates is x =73.0 beats per​ minute, and their standard deviation is sequals=23.2 beats per minute.   a. What is the difference between the pulse rate of 38 beats per minute and the mean pulse rate of the​ females? b. How many standard deviations is that​ [the difference found in part​ (a)]? c. Convert the pulse rate of 38 beats per minutes to a z score. d. If we consider pulse rates that convert to z scores between minus−2 and 2 to be neither significantly low nor significantly​ high, is the pulse rate of 38 beats per minute​ significant?