Question

Suppose the heights of 18-year-old men are approximately normally distributed, with mean 69 inches and standard deviation 4 inches. (a) What is the probability that an 18-year-old man selected at random is between 68 and 70 inches tall? (Round your answer to four decimal places.) (b) If a random sample of nineteen 18-year-old men is selected, what is the probability that the mean height x is between 68 and 70 inches? (Round your answer to four decimal places.) (c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this? O The probability in part (b) is much higher because the mean is smaller for the x distribution O The probability in part (b) is much lower because the standard deviation is smaller for the x distribution. O The probability in part (b) is much higher because the standard deviation is larger for the distribution. O The probability in part (b) is much higher because the mean is larger for the x distributiorn x The probability in part (b) is much higher because the standard deviation is smaller for the x distribution Need Help? Read It Submit Answer Save ress -1 points BBUnderStat12 6.5.015 My Notes Ask Your Teacher Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean μ = 74 and estimated standard deviation σ 31. A test result x 40 is an indication of severe excess insulin, and medication is usually prescribed (a) What is the probability that, on a single test, x < 40? (Round your answer to four decimal places.) (b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of X? Hint: See Theorem 6.1 O The probability distribution of x is approximately normal with μ-= 74 and = 31 O The probability distribution of x is approximately normal with x-74 and Ox-21.92 (D The probability distribution of x is approximately normal with x-74 and ơX-15.50 O The probability distribution of x is not normal What is the probability that x < 40? (Round your answer to four decimal places.) (c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.) (d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.) (e) Compare your answers to parts (a), (b), (c), and (d). Did the probabilities decrease as n increased? O Yes O No

Answer 1

Q 1)

Let X be the height of 18 year old man

X ~N (69, 4)

a)

b)

$P(68 <\overline{X}< 70) =P\left ( \frac{68-69}{4/\sqrt{19}}<Z<\frac{70-69}{4/\sqrt{19}} \right )$

c) The probability in part (b) is much higher because the standard deviation is smaller for the $\overline{x}$ distribution