Consider a nano ring consists of total 12 atoms as shown below. A black atom is initially placed at the outer rim of the ring as shown in the figure below. The black atom can randomly jump (with equal probability) from atom to atom along the outer side of the ring on either side as shown by the arrows. When the black atom passes by the grey atom, it emits a pulse of light with intensity I.. Compute the total average intensity of light emitted by the black atom in 15 jumps.
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- Please answer #12A poll found that 15% of adults do not work at all while on summer vacation. In a random sample of 8 adults, let x represent the number who do not work during summer vacation. Complete parts a through e.An automobile service facility specializing in engine tune-ups knows that 60% of all tune-ups are done on four-cylinder automobiles, 30% on six-cylinder automobiles, and 10% on eight-cylinder automobiles. Let X = the number of cylinders on the next car to be tuned. What is the pmf of X?
- Listed below are amounts of strontium-90 (in millibecquerels, or mBq) in a simple random sample of baby teeth obtained from residents in a region born after 1979. Use the given data to construct a boxplot and identify the 5-number summary. a. The 5-number summary is all in mBq. (Use ascending order. Type integers or decimals. Do not round.) b. Which boxplot below represents the data?A deck has "b" black cards and "y" yellow cards. Given that cards are drawn at a random fashion without replacement. Find the average where after drawing a black card it is immediately followed by a yellow cardAmorphophallus johnsonii is a plant called the "corpse flower" that grows in West Africa. Its flowers produce a pungent smell described as "a powerful aroma of rotting fish and faeces". It does so to attract its pollinator, the carrion beetle (Phaeochrous amplus) which live in rotting meat. Beath (1996) observed corpse flowers (hopefully wearing masks) and counted the number of beetles that arrived at each flower over the course of one night. The data is presented below: 51, 45, 61, 76, 11, 117, 7, 132, 52, 149 the mean of this sample is 70.1 beetles the standard deviation of this sample is 48.5 beetles Use the standard deviation of the sample to approximate the standard error of the mean. 1) What is the approximate SE that you calculated? Use the SE approximation method for normal sampling distributions to calculate Confidence Intervals 2) What are the 95% Confidence Intervals for this sample mean? 3) What are the 99% Confidence Intervals for this sample mean? 4) If an expanded…
- A 9-year-old girl did a science fair experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left hand, and then she asked the therapists to identify the selected hand by placing their hand just under her hand without seeing it and without touching it. A 9-year-old girl did a science fair experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left hand, and then she asked the therapists to identify the selected hand by placing their hand just under her hand without seeing it and without touching it. Among 257 trials, the touch therapists were correct 105 times. Use a 0.01 significance level to test the claim that touch therapists use a method equivalent to random guesses. Do the results suggest that touch therapists are effective?A neuroscientist wants to know if physical exercise changes reaction speed in elderly people. A total of 14 older volunteer participants were found. One sample of n = 7 subjects received an exercise treatment, while the second sample (n = 7) of participants were given stretching lessons for the same amount of time per week. Reaction speed was tested on a computer program after six weeks of treatment. Reaction speed was measured in milliseconds. Data shown below. What is the type of statistical test you could use on these data? _____________________ Why this test? ___________________________________________________________ What is the I.V.? ___________________ What is the D.V.? ______________________ Use the data below to fill in the blanks to compute your tcalculated. stretch group exercise group nstretch = ____ dfstretch = _____ nexercise…A medical researcher claims that the proportion of patients receiving 200 mg of a newly-developed influenza vaccine who go on to contract influenza strain X is less than the proportion of patients receiving 200 mg of last year's influenza vaccine who contract influenza strain X. Of 320 patients who are given last year's vaccine, 114 contract influenza strain X. Of 350 patients who are given the new vaccine, 112 of them contract influenza strain X. Let PN be the proportion of patients receiving the newly-developed vaccine and pL be the proportion of patients receiving last year's vaccine. State the null and alternative hypotheses and the value of the test statistic. Ho: PN =PL versus HA: PN > PL; Test statistic: Z = 0.99 Ho: PN=PL versus HA: PN > PL; Test statistic: Z = 1.55 Ho: PN-PL versus HA: PN PL; Test statistic: Z= 1.55 Ho: PN-PL versus HA: PN PL; Test statistic: Z= 0.99
- A company that manufactures medical devices is conducting tests in R&D on a new product. The product is in production on a pilot run (product will not be sold from the pilot run). The product is manufactured in batches and the quality of the batch must be determined, by testing a sample of 9 devices selected at random from a batch. One aspect that is monitored is the width of the bond in the device, ideally this should be equal to 3 mm on average. A sample from the latest batch gave the following bond widths measured in mm: 3.2, 2.8, 2.7, 3.0, 2.9, 2.9, 2.9, 3.2, 2.8 these gave an average of 2.93 mm and the widths varied by a standard deviation of s = 0.17 mm. Test, at significance level α = 0.01, whether there is evidence that the average bond width of the batch of devices is different to the required specification, by testing the following hypotheses: H 0: μ = 3 mm H a: μ ≠ 3 mm. Complete the test by filling in the blanks in the following:An estimate of the population mean is…Our bodies have a natural electrical field that is known to help wounds heal. Does changing the field strength slow healing? A series of experiments with newts investigated this question. In one experiment, the two hind limbs of 12 newts were assigned at random to either experimental or control groups. This is a matched pairs design. The electrical field in the experimental limbs was reduced to zero by applying a voltage. The control limbs were left alone. Here are the rates at which new cells closed a razor cut in each limb, in micrometers per hour (a) Make a stemplot of the differences between limbs of the same newt (control limb minus experimental limb). There is a high outlier. (b) A good way to judge the effect of an outlier is to do your analysis twice, once with the outlier and a second time without it. Carry out two t tests to see if the mean healing rate is significantly lower in the experimental limbs, one test including all 12 newts and another that omits the outlier.…Suppose that the students just completing freshman year at Galton University have Math SAT scores and first-year GPAS with the following summary statistics according to the registrar's office. Average Math SAT score = 540 SD = 100 Average first-year GPA = 2.6 r = 0.58 SD = 0.8 The scatterplot of their first-year GPAS on Math SAT scores is an oval-shaped cloud of points. Suppose a student from this freshman class at Galton University takes the SAT again during the summer and gets a score 75 points higher than his original score. By how much will his first-year GPA increase?