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P(-2.81>z>1.05)=
Smith et al. (A-5) performed a retrospective analysis of data on 782 eligible patients admitted with myocardial infarction to a 46-bed cardiac service facility. Of these patients, 248 (32 percent) reported a past myocardial infarction. Use .32 as the population proportion. Suppose 50 subjects are chosen at random from the population. What is the probability that over 40 percent would report previous myocardial infarctions?
Fifteen people sit around a circular table. What are odds against two particular people sitting together?
Find the probability that a leap year has 52 Sundays
Three dice are rolled together. What is the probability as getting at least one '4'
Two cards are drawn from the pack of 52 cards. Find the probability that both are aces
Jessica conducted a survey using a representative sample of 50 customers from three local landscaping businesses in town. She found that 30% purchased maple trees, 24% purchased dogwoods, 20% purchased oaks, 16% purchased pines and 10% chose other types of trees.
Which statements about the survey that Jessica conducted are most likely to be true? Select all that apply.
• Jessica surveyed only the customers who purchased a tree.
• Jessica asked customers what type of tree they purchased.
• Jessica asked customers what type of plants they have in their yards.
• The sample consists of 50 customers from three local landscaping businesses in town.
• The population Jessica wants to know about consists of any customer of any landscaping business
William passed an aptitude test in order to be accepted in law at McGill university. his result was 450, but the mean is 400, and the standard deviation is 75. His friend cassandra passed a similar but not identical test, in law again, but at l'univeristé de Montreal. her mark was 300, the mean is 200, and standard deviation.
Only the top 15% are selected for the program, are they going to be selected?
Suppose that
𝑇1 =(𝑋1 −𝜇)2
𝑇2 =1
2[(𝑋1 −𝜇)2 +(𝑋2 −𝜇)2]
And
𝑇3 =1
2(𝑋1 −𝑋2)2
Are estimators for 𝜎2.
i) Show whether or not 𝑇3 is an unbiased estimator of 𝜎2. (4)
ii) Which estimator is the most efficient between 𝑇1 and 𝑇2? (6)
d) Suppose that 𝑋1,𝑋2,...,𝑋𝑛 is a random sample from a distribution with
probability density function:
𝑓(𝑥;𝜃1,𝜃2)={
1
𝜃2
𝑒−𝑥−𝜃1
𝜃2 , 𝑖𝑓 𝑥 ≥𝜃1 𝑎𝑛𝑑−∞<𝜃2 <∞
0, 𝑒𝑙𝑠𝑒 𝑤ℎ𝑒𝑟𝑒
If 𝜃1 =0,
i) show whether or not ∑ 𝑋𝑖𝑛𝑖=1 is a minimal sufficient statistic for 𝜃2. (9)
ii) Show whether or not ∑ 𝑋𝑖𝑛𝑖=1 is a pivotal quantity. Give two reasons why or
why not it is a pivotal quantity. (5)
iii) What is the distribution of ∑ 𝑋𝑖𝑛𝑖=1 .
