1. Suppose that A and B are two mutually exclusive events in a sample space such that P(A) =1- P(B). Which ofthe following results regarding events A and B is false?(a) P(An B) = P(A)P(B).(b) P(ANB) = P(An).(c) P(A) = P(AnE)(d) P(B) = P(BnĀ).[Questions 2-3] Blue-Fly Airline took a random sample of n flights to determine the mean time it takes for luggage to reachthe travelers departing from a flight. The sample mean was found to be 8.2 minutes with a standard deviation of 3 minutes.Assume that the time in minutes has a normal distribution. Suppose that interest is in testing, at the 5% level of significance,whether the true mean time it takes for luggage to reach the travelers is less than 10 minutes.2. If T = -3, what is the numerical value of n?(а) 10.(b) 25.(c) 20.(d) 8.2.3. If 0.003 < p – value < 0.0035, which conclusion is correct?(a) Ho is not rejected and conclude that at the 5% level of significance there is insufficient evidence that themean time it takes for luggage to reach the travelers is less than 10 minutes.(b) Họ is rejected and conclude that at the 5% level of significance there is sufficient evidence that the meantime it takes for luggage to reach the travelers is less than 10 minutes.(c) Ho is not rejected and conclude that at the 5% level of significance there is sufficient evidence that the meantime it takes for luggage to reach the travelers is more than 10 minutes.(d) Họ is rejected and conclude that at the 5% level of significance there is insufficient evidence that the meantime it takes for luggage to reach the travelers is less than 10 minutes.4. Suppose we want to estimate the concentration (ug/mL) of a specific dose of ampicillin in the urine after variousperiods. We recruit 23 volunteers who have received ampicillin and find they have a mean concentration of 12.0ug/mL with a standard deviation of 4.4 ug/mL. Since the sample size is small, what assumption is needed toconstruct a 98% CI for the population standard deviation of the concentrations? Construct a 98% CI for thepopulation standard deviation of concentrations.(a) We must assume the population of concentrations is from a chi-squared distribution then the interval is:[10.5716; 44.6363].(b) We must assume the population of concentrations is from a t distribution then the interval is: [3.2514; 6.6810].(c) We must assume the population of concentrations is from an F distribution then the interval is:[3.2514; 6.6810].(d) We must assume the population of concentrations is from a normal distribution then the interval is:[3.2514; 6.6810).page 2 of 21Page Total:Version 40STA 1s1/1P1: September 2021page 3 of 215. Consider the following graph. Which statement is true?2220181614121050556070758085Variable 1(a) -1 [Questions 6-7| An animal scientist is investigating the distribution of a particular species from three different locations andcounted the number of female animals in each sample. The scientist would like to assess if these show a significant differencein the proportion of female animals in the three locations. The results are given below for 500 randomly selected animals.Use a = 0.05.| LocationNo. of FemalesTotal No. of animals | 100A BC86 110| 200442006. Which is the correct rejection region? That is we reject Ho if:(a) x, > xả0.05 = 5.991.(b) xab > xả0.025 = 7.378.(c) x < -xản 05 = -12.592.(d) x < -x2. 05 = -5.991.2,0.057. What is the correct numerical value of the test statistic for this test?(a) xá, = 6.5705.(b) x = 6.489.(c) x. = 5.991.(d) Xabs = 0.6410.page 3 of 21Page Total:Version 40STA 1s1/1P1: September 2021page 4 of 218. Suppose a lecturer sets up a probability question for an upcoming exam. He defines A and B as two eventssuch that P(A) = 0.8 and P(B) = 0.7. He then defines P(An B) = 0.76. Is this an appropriate value forP(An B)?(a) Yes, since P(AU B) = 0.74 and all other probabilities specified in the question satisfy probability laws.(b) No, since P(An B) cannot be larger than either of P(A) or P(B) and in this case will result in a negativevalue for P(BnĀ).(c) No, since A and B are mutually exclusive and the probability of the union of evets A and B is greater thanone and this violates probability laws.(d) Yes, since P(A), P(B) and P(An B) are all between zero and one.9. Suppose that A and B as two events such that P(A) = 0.60, P(B) = 0.45 and P(Au B) = 0.60. DetermineP(Ān B).(a) 0.35.(b) 0.40.(с) 0.65.(d) 0.22.

Name: 1. Suppose that A and B are two mutually exclusive events in a sample
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Description: 1. Suppose that A and B are two mutually exclusive events in a sample space such that P(A) =1- P(B). Which ofthe following results regarding events A and B is false?(a) P(An B) = P(A)P(B).(b) P(ANB) = P(An).(c) P(A) = P(AnE)(d) P(B) = P(BnĀ).[Questi