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1. Consider the following ordered pairs:
(Ã¢Ë†â€™2, Ã¢Ë†â€™6.2), (1, 7.2), (4, 17.4), (7, 14.5)
(i) Calculate the linear correlation coefficient r. Is the correlation strong?
(ii) Compute the regression line.
(iii) Use the regression line to estimate the y-coordinate when x = 6.
2. In the US, the shoe size of women is normally distributed with mean 8 inches and a
standard deviation of 1.5 inches.
(i) What is the percentage of women in the US with shoe size between 6 inches and
(ii) What is the percentage of women with shoe size greater than 10.5 inches?
3. The weight of a new species of wolf is normally distributed with a mean weight of
Ã‚Âµ = 160 lbs and a standard deviation of ÃÆ’ = 25 lbs. This new species of wolf has
been called a blue wolf. What is the 80th percentile for the weight of the blue wolf?
4. The average height of redwood trees in the Pacific Northwest is 360 feet with a
standard deviation of 80 feet. A sample of 35 redwood trees is selected. Let x denote
the mean height of the sample.
(i) What is the probability that x is between 350 feet and 380 feet?
(ii) What is the probability that x is greater than 395 feet?
5. In the US, 29% of the population suffers from back pain. 140 people are chosen at
random. Let pb be the proportion of the sample with back pain. What is the probability that pb will between 25% and 32%?
6. Greyhound bus says they arrive at their destination on time 90% of the time. In a
random sample of 230 Greyhound buses, it was found that only 200 arrive on time.
(i) Assuming GreyhoundÃ¢â‚¬â„¢s claim is true, compute the probability of getting a sample
of size 230 with a sample proportion as low as the one observed in this sample.
(ii) Based on your calculation in (i), do you believe GreyhoundÃ¢â‚¬â„¢s claim?
7. A new surgical procedure for repairing disc herniations is developed. In a random
sample of 150 of these operations, 104 were a success. Calculate the 96% confidence
interval for the proportion of these types of operations which were a success.
8. A sample of 40 female giraffes are chosen. The mean height is found to be 15 feet.
Assume that the population standard deviation for the height of female giraffes is
ÃÆ’ = 5 feet. Calculate the 95% confidence interval of for population mean height of
9. In a random sample of 20 male grizzlies, the sample mean was found to be 550 pounds
and the sample standard deviation was found to be 30 pounds. Calculate the 90%
confidence interval for the population mean weight of male grizzlies. Assume that the
weight of male grizzles are normally distributed.
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