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- I need help with all of them plz.You own a local company that has special equipment for moving pianos. Your company has enough equipment to handle three pianos in a day. The number of requests to move pianos is a random variable with following distribution. → x f(x) 0 0.30 1 0.38 2 0.15 3 4 0.05 5 0.03 6 0.01 3 The probability that some of your equipment will be idle is ______. The probability that you receive less than 3 requests. a 0.80 b 0.81 c 0.82 d 0.83please explain!
- A team of researchers working on the development of vaccines conducted a study on two vaccines. Thirty individuals participated in the study and were randomly assigned to two groups and one group received vaccine 1 and the other group vaccine 2. The researchers then measured the amount of antibody in the individuals' blood after ingestion, entered R and calculated some fish sizes that can be seen here below. x̄1 = 494,54, s1 =52,39, x̄2 = 467,93, s2 = 45,20, d = 26,61, sd = 68,69. Blood levels of antibodies can be expected to follow normal distribution. Use α = 0,05. c) What conclusion do you draw from the hypothesis test in point b about the possible difference in the mean amount of antibody after oral administration of the vaccines? d) The researchers also created a 95% confidence interval for the difference between the averages. Will the confidence interval contain the value 0? Justify your answer without calculating the confidence interval.e) Let us now assume that there is in fact…A certain medical school accepts only 8% of applicants. A prep program claims that their students are admitted to this medical school at a higher rate. To test their claim at the 10% significance level, we select at random 144 students from the prep program (who all apply to this medical school), and we compute p, the proportion of the sample who are admitted to the medical school.Find the number of ways in which one A, three B’s, two C’s, and one F can be distributed among seven stu-dents taking a course in statistics.
- Katy is interested to understand the of herd immunity concept for Singapore's COVID-19 cases. She noted that 95% of adult population in Singapore's is fully vaccinated by the end of October 2021. She want to compare difference of COVID-19 death cases in Singapore's before Singapore's achieve herd immunity and after Singapore's achieve herd immunity. She collects the data of death cases in Singapore's two weeks in the early of October 2021 (to represent before herd immunity) and two weeks in the end of November 2021 (to represent after herd immunity). Assume the variable is approximately normally distributed. The data are presented as below. Before herd immunity After herd immunity 121 109 118 76 117 105 132 53 40 68 55 45 41 24 78 74 64 93 103 68 88 63 47 37 48 45 40 29 a) What test is appropriate to be used in this question? State why. b) Find sample mean and sample standard deviation of the above data. c) Can Katy concluded that the before herd immunity death cases is lower than the…Biologists in Minnesota are interested in determining if there is a difference in the invasion rate of Asian Carp (which can be detrimental to the environment) between the Mississippi River and Lake Mille Lacs. In the Mississippi River, it was found that 206 of 579 fish caught were Asian Carp. In Lake Mille Lacs, 28 of 132 fish caught were Asian Carp. Let p, = the true proportion of Asian Carp in the Mississippi River and let p2 = the true proportion of Asian Carp in Lake Mille Lacs. A test of Ho: P₁ = P2 vs. Ha: P₁ P₂ resulted in a p-value of 0.0015. Which of the following is a correct conclusion? (A) The test is not appropriate, since the researchers should have conducted a one-sided test. (B) The test is not appropriate, since the sample size is too small to conduct an inference test for proportions. (C) The test is not appropriate, since the two sample sizes are very different. (D) The p-value of this test is large, indicating we have sufficient evidence to conclude that a…A study of n = 2252 adults age 18 or older found that 72% of the cell phone users send and receive text messages.15 A study of n = 800 teens age 12 to 17 found that 87% of the teen cell phone users send and receive text messages. What is the best estimate for the difference in the proportion of cell phone users who use text messages, between adults (defined as 18 and over) and teens? Give notation (as a difference with a minus sign) for the quantity we are trying to estimate, notation for the quantity that gives the best estimate, and the value of the best estimate. Be sure to clearly define any parameters in the context of this situation.
- A researcher wants to determine the specificity of mammograms to determine how effective they are at diagnosing women who have breast cancer. Assume the researcher obtained the results below from a study: Out of a total of 18 women with breast cancer, 12 screened positive and 6 screened negative on the mammogram. Out of a total of 82 women without breast cancer, 5 screened positive and 77 screened negative on the mammogram. Calculate and interpret the specificity of mammograms for detecting breast cancer.Suppose that a researcher is studying the wingspans of wild condors. To study this the researcher randomly selects 7 condors that live near the California Coast and 7 condors that live near the Grand Canyon for a total of 14 condors. The researcher measures the wingspan of each of these birds in inches and gets the following data. (Note: You may assume that there are about 400 condors in the wild) 94, 100, 102, 110, 115, 118, 119, 122, 123, 126, 128, 135, 136, 140 (All values in inches) (a) What sampling technique was used to collect this data? (b) Use this data to construct a 99% confidence interval for the average wingspan for California condors. Make sure to confirm all necessary conditions and interpret your interval. (Hint: This should be a 1-sample mean confidence interval) (c) Could you conclude that 99% of California condors will have wingspans inside the interval you found in (b)? Why or why not?