Question

in 214 Section Hicach domow page in your blue bok Only wor k will be add must show your work where every to reveu This includes Functions that you may use in your calculo You MUST give the name of the union, AND the param o input into each function 1. Find the following areas under the standard normal curve. Round answers to four decimal a) the area to the left of 2-0.64. h) the area to the right of 2 -1.23. c) the area that lies between 1.02 and 0.19 d) the area that lies outside the interval from 0.73 to 1.55 2. Suppose that the heights of pecan Trees in a specific region are normally distributed with a mean of 41 feet and a standard deviation of 8.2 feel a) What is the oth percentile of the heights of the pecan trees? Round to one decimal place and include correct units. b) What is the probability that a randomly selected pecan tree has a height between 39 feet and 42 feet. Round to four decimal places. c) What is the probability that a randomly selected pecan tree has a height greater than 45 feet? Round to four decimal places d) Would it be unusual for a randomly selected pecan tree to have a height greater than 45 feet? (Use the textbook's definition of unusual) c) What is the probability that the mean height of a simple random sample of 36 pecan trees will be greater than 45 feet? Round to four decimal places Would it be unusual for the mean height of a simple random sample of 36 pecan trees to be greater than 45 feet? (Use the textbook's definition of unusual.) 3. Suppose that eight percent of men in a certain region are colorblind. A simple random sample of 140 men in the region were sampled a) Find the probability that the proportion of men in the sample who are colorblind is between 0.06 and 0.127 Round to four decimal places. b) Find the probability that the percentage of men in the sample who are colorblind is less than 10%. Round to four decimal places. 4. Suppose that the ages of diabeties in a particular population are approximately normally distributed. A simple random sample of 56 diabetics from this particular population is taken and a 95% confidence interval for the population mean age is found to be 49.5 years to 73.5 years. a) What is the margin of error for the confidence interval? b) Would a 99% confidence interval be wider than the 95% confidence interval? c) If the sample size was increased and everything else remained the same, would confidence interval be wider or narrower?

Answer 1

Solution:

1.
a) P(Z < 0.64) = 0.7389

b) P(Z > -1.23) = P(Z < 1.23) = 0.8907

c) P(-1.02 < Z < 0.89) = P(Z < 0.89) − P(Z < −1.02)
= 0.8133 - 0.1539
= 0.6594

d) out side the interval from z = -0.73 to 1.55 = 0.2933

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3. Given that p =0.08, n = 140

a) P(0.06 < p^ < 0.12) =
= P((0.06-0.08)/sqrt(0.08*0.92/140) < (p^-p)/sqrt(pq/n) < (0.12-0.08)/sqrt(0.08*0.92/140)
= P(-0.8722 < Z < 1.7445
= 0.7669

b) P(X < 0.10) = P(Z < (0.10-0.08)/sqrt(0.08*0.92/140))
= P(Z < 0.8723)
= 0.8078

note : 2 question was note clear.