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**Review for 2nd Nine Weeks Test**

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**The distribution of SAT Math scores of students taking **

Calculus I at UTSA is skewed left with a mean of 625 and a standard deviation of If random samples of 100 students are repeatedly taken, which statement best describes the sampling distribution of sample means? A) Shape is normal with a mean of 625 and standard deviation of 44.5. Shape unknown with a mean of 625 and standard deviation of 44.5. Shape unknown with a mean of 625 and standard deviation of 4.45. E) No conclusion can be drawn since the population is not normally distributed. B) Shape is normal with a mean of 625 and standard deviation of 4.45.

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**Answer Formula: 𝜎 2 𝑛 44.5 2 100 Or simply: 𝜎 𝑛 44.5 100**

Or simply: 𝜎 𝑛 These answers are the same

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2) A population has a normal distribution with a mean of 50 and a standard deviation of 10. If a random sample of size 9 is taken from the population, then what is the probability that this sample mean will be between 48 and 54? A) B) C) 0.385 D) 0.399 E) 0.611

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**Answer P(48< 𝑥 <54)= 48−50 10 9 <Z< 54−50 10 9**

P(-.6< 𝑥 <1.2) = (Z score for -.6) + (Z score for -1.2) = = Normalcdf(-.6, 1.2) =

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3) Owners of a day-care chain wish to determine the proportion of families in need of day care for the town of Helotes. The owners of the day-care chain randomly sample 50 Helotes families and find only 4% of the returned questionnaires indicate these families having a need for child day-care services. The 4% is best described as the sample proportion of families in Helotes needing child day-care services. B) the sample proportion of families in Helotes with children needing day-care services. C) the population proportion of families in Helotes with children needing day-care services. D) the 30 families in Helotes needing day-care services for their children. E) the 600 families in Helotes with children needing day-care services.

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Answer Since the survey was to indicate the families having a need for child day-care services, that is what the 4% represents.

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A coach in a large high school thinks that ballet training will improve the batting performance of his baseball team. He decides to have a randomly selected half of the team take six weeks of ballet training before the baseball season begins while the other half does not take such training. He will then compare the season batting averages of group A (those with ballet training) and group B (those without ballet training) by comparing the mean of group A with the mean of group B. 4) This study would be classified as: a. a survey b. an observational study c. an experimental study

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Answer Study has a treatment, so it can not be observational. It obviously is not a survey.

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A coach in a large high school thinks that ballet training will improve the batting performance of his baseball team. He decides to have a randomly selected half of the team take six weeks of ballet training before the baseball season begins while the other half does not take such training. He will then compare the season batting averages of group A (those with ballet training) and group B (those without ballet training) by comparing the mean of group A with the mean of group B. 5) The response variable is: a. ballet training c. runs batted in d. the size of the school e. the grades the players make in the ballet school b. batting average

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Answer Response variable is like a dependent variable...batting average is dependent.

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**If P(A) = 0.24 and P(B) = 0.52 and events A and B are independent, what is P(A or B)?**

e) The answer cannot be determined from the information given. c)

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**Answer P(A or B) = P(A) + P(B) - P(A and B) As A and B are independent**

P(A and B) = P(A)P(B). So, P(A or B) = x.52 = .6352

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7) Before premiering a blockbuster movie at a theater, test screenings are done beforehand. A small number of selected theaters are chosen geographically throughout the country. Each theater chosen is supposed to be representative of theatergoers in that area. Everyone is interviewed when the movie is over. Identify the type of sampling used in this example. Stratified sampling B) SRS D) Systematic Sampling E) Convenience Sampling C) Cluster Sampling

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Answer Since a small number of theatres are chosen in a location geographically and then a census is done to that sample this is cluster sampling.

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**8) A test consists of 10 true/false questions**

8) A test consists of 10 true/false questions. If a student guesses on each question, what is the probability that the student will answer at least 9 questions correctly? 0.9 B) C) 0.010 D) 0.999 E) 0.011

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Answer This is a problem on binomial probabilities. The probability of success (correct answer) p is 0.5; respectively the probability of failure is also 0.5. The number of experiments n is 10. We are interested in probability that the number of successes is at least 9 P(X≥9) = P(X=9) + P(X=10) 10 𝐶 9 = ( 1 2 ) 9 ∙ 1− −9 + ( 1 2 ) 10 ∙ 1− −10 At least 9 would be 9, or 10 so you'd have to do each then add the answers. Formula is nCr p^x q^ (n - x) where n = total possible x = number of successes p = probability of success q = prob. of failure Binompdf(10, .5, 9)+binompdf(10, .5, 10) =

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9) A basketball player has made 66% of his foul shots during the season. Assuming the shots are independent, find the probability that in tonight's game he misses for the first time on his 6th attempt? A) B) C) D) E) 0.34

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**Answer Geometric P(miss, q) = .34, P(makes, p) = .66,**

P(x = 1) = geometpdf(.34, 6) or simply (.66)^5(.34)

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**Calculate the following (show your work):**

At George Washington High School students are heavily involved in extra-curricular activities. Suppose that a student is selected at random from the students at this school. Let the events A, M, and S be defined as follows, with probabilities listed: A = student is active in the performing arts: P(A) = 0.20 M = student is active in vocal or instrumental music: P(M) = 0.32 S = student is active in sports: P(S) = 0.35 ∩ ∩ Calculate the following (show your work): ∩

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**2ND Nine weeks Review – Ch 11-18**

B 2) E 3) A 4) C 5) B 6) C 7) C 8) E 9) A

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