Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)   P(−2.14 ≤ z ≤ −0.35) =  Shade the corresponding area under the standard normal curve.

X has a normal distribution with the given mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) ? = 56, ? = 10, find  P(36 ≤ X ≤ 66)

Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml). 91 88 82 103 97 108 84 91 The sample mean is x ≈ 93.0. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we know from past experience that ? = 12.5. The mean glucose level for horses should be ? = 85 mg/100 ml.† Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use ? = 0.05.   (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: ? = 85; H1: ? > 85; right-tailed   H0: ? > 85; H1: ? = 85; right-tailed      H0: ? = 85; H1: ? ≠ 85; two-tailed   H0: ? = 85; H1: ? < 85; left-tailed   (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.…

Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.) P(−1.75 ≤ z ≤ −1.27)  = Shade the corresponding area under the standard normal curve.