Use this information about the overhead reach distances of adult females: µ = 205.5 cm, σ = 8.6 cm, and overhead reach distances are normally distributed (based on data from the Federal Aviation Administration). The overhead reach distances are used in planning assembly work stations. If 49 adult females are randomly selected, find the probability that they have a mean overhead reach less than 207.0 cm.

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 139 120 128 64 78 April 108 113 102 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?State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H0: ?d > 0; H1: ?d = 0; right-tailedH0: ?d = 0; H1: ?d ≠ 0; two-tailed    H0: ?d = 0; H1: ?d < 0; left-tailedH0: ?d = 0; H1: ?d > 0;…

Assume that adults have IQ scores that are normally distributed with a mean of u= 100 and a standard deviation o= 15. Find the probability that a randomly selected adult has an IQ less than 130. Click to view page 1 of the table. Click to view page 2 of the table. The probability that a randomly selected adult has an IQ less than 130 is (Type an integer or decimal rounded to four decimal places as needed.)

Assume that women's weights are normally distributed with a mean given by mean=143 lb and a standard deviation given by 29 lb. If 3 women are randomly selected, find the probability that they have a mean weight below 113 If 85 women are randomly selected, find the probability that they have a mean weight below 113