Consider an experiment with sample space S = {A,B,C}. If P(A)=0.3, P(B)=0.5, and P(C)=0.2, then (a) P( A or C ) = (b) P( B and C ) =
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Consider an experiment with
If P(A)=0.3, P(B)=0.5, and P(C)=0.2, then
(a) P( A or C ) =
(b) P( B and C ) =
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- A box contains 5 green and 3 orange balls. If three balls are taken at random with replacements, what is the variance number of orange balls? A. 45/8 B. 15/8 C. 1/8 D. 9/8When two births are randomly selected, the sample space for genders is bb, bg. gb, and gg. Assume that those four outcomes are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from two births. Does the mean of the sample proportions equal the proportion of girls in two births? Does the result suggest that a sample proportion an unbiased estimator of a population proportion? For the entire population, assume the probability of having a boy is the probability of having a girl is , and this is not affected by how many boys or girls have previously been born. 2 Determine the probabilities of each sample proportion. Probability Sample proportion of girls Tune intanare or cimnlifiad frartinneSuppose that Mairin has knit a collection of wool‑blend infinity scarves that she wants to sell in her Etsy shop for $28.00 each. However, she is worried that if the average price of comparable scarves is less than $28.00, hers would be less likely to sell. Mairin selected a random sample of 9 similar hand‑knit, wool‑blend infinity scarves, and their prices are as follows. $21.75,$24.00,$27.25,$29.95,$23.00,$26.00,$27.80,$33.50,$27.00$21.75,$24.00,$27.25,$29.95,$23.00,$26.00,$27.80,$33.50,$27.00 Use a left‑tailed one‑sample ?t‑test to determine whether the average price of hand‑knit, wool‑blend infinity scarves sold on Etsy is less than $28.00. Assume that the prices of all comparable scarves are normally distributed. Mairin should (reject, accept, fail to accept) her null hypothesis. There is (sufficient, no, insufficient) evidence that the mean price of hand‑knit, wool‑blend infinity scarves is (greater than, different from, less than, equal two) $28.00.
- The records of a light bulb manufacturer show that, when the manufacturing machinery is working correctly, the defect rate (due to imperfections in the material used) is 1%. The manufacturer's control department periodically tests samples of the bulbs, and when 1.25% or more are defective, they call repair technicians for service. The control department is going to take a random sample of 4400 light bulbs. Let p be the proportion of defective light bulbs in the sample assuming the machinery is working correctly. A) find the mean of p b)find the standard deviation of p c)Compute an approximation for P≥p0.0125, which is the probability that, assuming the machinery is working correctly, the repair technicians will be called. Round your answer to four decimal places.The records of a light bulb manufacturer show that, when the manufacturing machinery is working correctly, the defect rate (due to imperfections in the material used) is 1%. The manufacturer's control department periodically tests samples of the bulbs, and when 1.25% or more are defective, they call repair technicians for service. The control department is going to take a random sample of 4400 light bulbs. Let p be the proportion of defective light bulbs in the sample assuming the machinery is working correctly. Answer the following. (If necessary, consult a list of formulas.) (a) Find the mean of p. (b) Find the standard deviation of p. (c) Compute an approximation for P(P ≥ 0.0125), which is the probability that, assuming the machinery is working correctly, the repair technicians will be called. Round your answer to four decimal places.A survey is conducted to determine if there is a difference in the proportion of students, parents, and What are the appropriate hypotheses to determine if the distribution of response differs among these three populations? teachers who volunteer at least once a month. To investigate, a random sample of 45 students, 25 parents, and 12 teachers was selected from a large high school. The data are displayed in the table. O Ho: There is a difference in the distribution of responses among these three populations. Hg: There is no difference in the distribution of Student Parent Teacher responses among these three populations. 12 O Ho: There is no difference in the distribution of Yes 24 Volunteer? responses among these three populations. Hg: There is a difference in the distribution of No 21 13 response among these three populations. Họ: There is no association between the type of person who is surveyed and the response. Hạ: There is an association between the type of person who is surveyed…
- The candy company that makes M&M's claims that 10% of the M&M's it produces are green. Suppose that the candies are packaged at random, and the small bags contain 25 M&M's. When we randomly pick a bag of M&M's, we may assume that this represents a simple random sample of size n = 25. Suppose that in a randomly selected small bag of M&M's, there are 5 green M&M's. What is the value of the standard error of p? 0.08 0.0063 0.0794 O 0.10Sample space S is partitioned into E1, E2, E3, and E4 such that P(E,) = 0.28, P(E2) = 0.03, and P(E3) = 0.48. %3D a. Find P(E4). b. Find the odds in favor of and the odds against E, occurring. ..... a. P(E4) = (Simplify your answer.) %3D b. The odds in favor of E4 occurring, in lowest terms, are (Type whole numbers.) The odds against E4, in lowest terms, are (Type whole numbers.)46% of all statistics classes require an advanced calculator and 38% require the use of a computer that has statistical software. Of the classes that require an advanced calculator, 18% also require the use of a computer. If a statistics course is selected at random find A. P(Advanced Calculator) = [ Select ] ["0.57", "0.38", "0.18", "0.46"] B. P(Statistical Software) = [ Select ] ["0.38", "0.57", "0.46", "0.18"] C. P(Require an Advanced Calculator and Statistical Software) = [ Select ] ["0.1259", "0.1748", "0.0828", "0.8335"] D. P(Require an Advanced Calculator GIVEN Require Statistical Software) = [ Select ] ["0.3515", "0.18", "0.2184", "0.9716"]
- 3. The following experiment was carried out to evaluate a drug for the prevention of heart attacks. The subjects were 3,900 middle-aged men with heart trouble. Out of these men, 1,100 were assigned at random to receive the drug, and the remaining 2,800 were given a placebo. The subjects were followed for five years. In the group that received the drug, there were 220 deaths; in the placebo group, there were 588 deaths. Note that 220 is 20% of the treatment group, and 588 is 21% of the control group. Someone argues as follows: “A 1% difference may not seem like much, but 1% of a million, for example, is 10,000. The drug will save tens of thousands of lives.” Should we be convinced by the difference between the two groups, or do you think the results are just due to chance? Carry out all the steps of a hypothesis test and state your conclusion.Suppose that we have a sample space with five equally likely experimental outcomes: E1, E2, E3, E4, E5. Let A = {E1, E4} B = {E2, E3} C = {E2, E4, E5}. (a) Find P(A), P(B), and P(C). P(A) = P(B) = P(C) = (b) Find P(A ∪ B). P(A ∪ B) = Are A and B mutually exclusive? They mutually exclusive. (c) Find AC. (Enter your answer in set notation.) AC = Find CC. (Enter your answer in set notation.) CC = Find P(AC) and P(CC). P(AC) = P(CC) = (d) Find A ∪ BC. (Enter your answer in set notation.) A ∪ BC = Find P(A ∪ BC). P(A ∪ BC) = (e) Find P(B ∪ C). P(B ∪ C) =p3
