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Math 1121 Quiz 3 Practice
- The height of all the 12-year-old girls in Canada is distributed as shown.
128.75 136.25 143.75 151.25 158.75 166.25 173. Height (cm)
34% 34% 13.5% 13.5% 0.5% 2%^ 2% 0.5%
What is the probability that a girl chosen at random from that age group will have a height more than 128.75 centimeters?
- The scores for a standardized reading test are found to be normally distributed with a mean of 400 and a standard deviation of 44. If the test is given to 500 students, how many are expected to have scores between 400 and 444?
- Adeline’s z score on a biology final is 0.6. If the raw scores have a mean of 475 and standard deviation of 46 points, what is her raw score? Round to nearest tenth.
- What is the area under the standard normal curve to the left of (^) z 132.?
–1.32 0
- The running times of feature movies have a mound shaped distribution with mean P = 110 minutes and standard deviation V = 30 minutes. (a) Use the empirical rule to find an interval centered about the mean in which 68% of the data will fall. (b) Estimate a range of values centered about the mean in which about 95% of the data will fall.
- Weights of Pacific yellowfin tuna follow a normal distribution with mean weight 68 lb and standard deviation 12 lb. A Pacific yellowfin tuna is caught at random. (a) Find the probability that its weight is less than 48 lb. (b) Find the probability that its weight is more than 100 lb. (c) Find the probability that its weight is between 48 lb and 100 lb.
- Which of the following ranges of values corresponds to a probability of 0.8213?
[A] –1 d d 1.
[B] –1.13 d d 1.
[C] –1.65 d d 2
[D] –1 d d 1
[E] –1.13 d d 1.
- Records at the College of Engineering show that 62% of all freshmen who declare EE (electrical engineering) as their intended major field of study eventually graduate with an EE major. This fall, the College of Engineering has 316 freshmen who have declared an EE major. (a) What is the probability that between 200 and 225 of them (including 200 and 225) will graduate with an EE major? (b) Can you use a normal approximation to the binomial distribution to estimate this probability? Explain.
- Roger has read a report that the weights of adult male Siberian tigers have a distribution which is approximately normal with mean P = 390 lb. and standard deviation V = 65 lb. (a) Find the probability that an individual male Siberian tiger will weigh more than 450 lb. (b) Find the probability that a random sample of 4 male Siberian tigers will have sample mean weight more than 450 lb.
- The electric company has estimated that the mean number of kilowatts of electricity used by a household per month is 365 kW with standard deviation 30 kW. To check their estimates a random sample of 40 households was chosen. (a) If the power company’s estimates are correct, find the probability that the sample mean amount of electricity will be between 358 and 372 kW. (b) If the actual sample mean was 385 kW would you question the power company’s figures? Explain.
- Suppose we have a binomial distribution with n = 40 trials and probability of success p = 0.38. The random variable r is the number of successes in the 40 trials, and the random variable
representing the proportion of successes is = r / n.
(a) Compute P (0.30 d d 0.40).
(b) Compute P ( t 0.40).
(c) If p = 0.12, can we approximate by a normal distribution? Explain.
Note: Approximate all values except -values to four decimal places.
- Compute an 85% confidence interval for the following situation: Out of 160 basketballs purchased, 16 have leaks. Let p represent the proportion of basketballs with leaks to all basketballs produced by the manufacturer.
[A] 0.07 < p < 0.
[B] 0.06 < p < 0.
[C] 0.08 < p < 0.
[D] 0.05 < p < 0.
[E] 0.09 < p < 0.
- For a particular research project, the maximum error of estimate must be no larger than 0. unit, with a confidence level of 99%. A preliminary sample study produced a sample standard deviation of s = 2.5 units. How large must the sample taken be to ensure the above requirements for the research project?
[A] 4161
[B] 64
[C] 65
[D] 4160
[E] 2081
- (^) x (^) 1 has a normal distribution with mean (^) P 1 = 21.1 and standard deviation (^) V 1 = 3.1. (^) x 2 has a
normal distribution with (^) P 2 = 13.4 and (^) V 2 = 2.2. Independent random samples of size (^) n 1 = 90
was taken from (^) x 1 and (^) n 2 = 110 from (^) x 2.
(a) Does the variable (^) x (^) 1 x 2 have a normal distribution?
(b) What is the mean of (^) x (^) 1 x 2?
(c) What is the standard deviation of (^) x (^) 1 x 2?
- A business finance class is studying start-up costs for various kinds of small businesses. A random sample of 9 sports equipment and apparel stores had sample mean start-up costs (in thousands of dollars) of 91.0 with sample standard deviation 33.92. An independent random sample of 10 travel agencies had sample mean start-up costs of 61.5 with sample standard deviation 34.03. (a) Find a 90% confidence interval for the difference in population mean start-up costs for the two types of businesses. (b) Does it seem likely that there is a difference? Explain.
- In January 2001, a random sample of registered voters in a city was asked whether or not they approved of the job the mayor was doing. Three hundred thirty-six out of the 600 polled said they approved. In July 2001, another random sample of registered voters in the city was asked the same question. This time, 210 out of the 500 polled said they approved. Compute a 95% confidence interval for (^) p (^) 1 p 2 , the difference of proportions of registered voters who
approved of the mayor’ s performance relative to all registered voters. Let (^) p 1 represent the
proportion from January and (^) p 2 from July.
[A] 0.11 < (^) p 1 (^) p 2 < 0.
[B] 0.08 < (^) p 1 (^) p 2 < 0.
[C] 0.139 < p 1 (^) p 2 < 0.
[D] 0.12 < (^) p 1 (^) p 2 < 0.
[E] 0.138 < (^) p (^) 1 p 2 < 0.
[10] (a) P (358 d (^) x d 372) = 0.
(b) P ( (^) x t 385) = 0.0000 to four decimal places. The sample mean is unlikely to be as high as 385kW if the electric company’ s figures are correct.
Reference: [7.92] [11] (a) 0. (b) 0. (c) No; np < 5.
Reference: [8.17] [12] 92
Reference: [8.10] [13] (^116). P 9 26.
Reference: [8.27] [14] [C]
Reference: [8.29] [15] [A]
Reference: [8.97] [16] [A]
Reference: [8.100] [17] [A]
Reference: [8.114] [18] (a) Yes (b) 7. (c) 0.
Reference: [8.116] [19] (a) Interval for (^) P 1 P 2 from 2.34 thousand to 56.7 thousand
(b) Yes. The interval contains only positive numbers. We can say with 90% confidence that
P 1 > P 2.
Reference: [8.136] [20] [B]
