1. Two growth hormones are being considered. A random sample of 10 rats was given the first hormone and the average weight gain was x1 = 2.3 pounds with a standard deviation s1 = 0.4 pound. For the second hormone, a random sample of 15 rats had an average weight gain of x2 = 1.9 pounds with a standard deviation s2 = 0.2 pound. Assume the weight gains follow a normal distribution. Find the 90% confidence interval for the difference in average weight gain for the two growth hormones.
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a. 0.20 to 0.60 pounds
b. 0.17 to 0.63 pounds
c. 0.15 to 0.65 pounds
d. 0.24 to 0.56 pounds
2. The manufacturer of a coffee dispensing machine claims that the ounces per cup dispensed is mound shaped and symmetric with a mean u = 7 ounces and standard deviation o = 0.8 ounce. If 40 cups of coffee are measured, what is the probability that the average ounces per cup is between 6.8 and 7.4 ounces?
3. A random sample of 47 manuscripts typed by Katlyn showed that 13 of them had errors. A random sample of 85 manuscripts typed by Dara showed that 31 of them had errors. Find a 99% confidence interval for the difference in the proportion of all manuscripts with errors typed by Katlyn compared to those typed by Dara.
a. -0.323 to 0.146
b. -0.252 to 0.076
c. -0.887 to 0.711
d. -0.303 to 0.127
4. A manufacturing company produces electric insulators. If the insulators break in use, a short is likely to occur. Thus, destructive testing is carried out to determine how much force is required to break the insulators. Suppose you wish to estimate the mean force required to break the insulators to within +- 25 pounds with 95% confidence. If on the basis of a study taken the previous year, you believe that the standard deviation is 100 pounds, find the sample size needed. Place your answer, rounded up to the next highest whole number.
5. Studies have shown that 24% of all students at Sky High School smoke. Suppose we happen to observe a random sample of 70 students in the school courtyard. What is the probability that the proportion of those 70 student in the courtyard who smoke is no more that 20%?
6. Assuming the weights of newborn babies at a certain hospital are normally distributed with mean 6.5 pounds and standard deviation 1.2 pounds, how many babies in a group of 80 babies for this hospital will weigh more than 8.9 pounds? Round your answer to the nearest whole number.
7. The diameter of oranges from a Florida orchard are normally distributed with mean u = 3.2 inches and standard deviation o = 1.1 inches. A packing supplier is designing special occasion presentation boxes for oranges and needs to know the average diameter for a random sample of 8 oranges. If a random sample of 8 oranges is to be taken from this orchard, what is the probability that the mean diameter of those oranges will be smaller than 3 inches? Round your answer to 4 decimal places.
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