Watch help video When Ian commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 59 minutes and a standard deviation of 3 minutes. What percentage of his commutes will be longer than 54 minutes, to the nearest tenth? Statistics Calculator
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- a. Is Y discrete or continuous? Explain. Plot the PMF/PDF of random variable Y (whichever is applicable).b. What is the value of P[1 < Y ≤ 4]distributions of both Y1 and Yn are uniform and continuoushe length of time, in minutes, for an airplane to obtain clearance for takeoff at a certain airport is a random variable Y = 3X-2, where X has the density function. Find the mean and variance of the random variable Y.
- The continuous random variable X has cumulative distribution function a. Find the PDF, fX(x) b. Determine the E(X) and Var(X) c. Find the median or the 50th percentilesolve the problem in the photo using normal distribution lawsA study was conducted in the tidal flat at Polka Point, North Stradbroke Island to examine the distribution of the animals that live with the seagrass Sargassum at different distances from the shoreline. Samples of Sargassum were taken at 5, 10, 15 m from the shore and these were examined for amphipods and isopods. The observations are recorded below. Is the distribution of each of the organisms with regards to the shore the same at all three distances? Use the data below to test the hypothesis at the p < 0.05 level. Clearly state the hypotheses and interpret the results. (Note: Find chi-square for each individual column (amphipods and isopods, not the two together) Distance Amphipods Isopods 5 2 7 10 31 14 15 45 22
- Assuming that the data are normally distributed, A. Determine the z-score such that the area to its right is 17%. z = B. Determine the z-score such that the area to its left is 95%. z =Researchers wanted to determine if carpeted rooms contained more bacteria than uncarpeted rooms. To determine the amount of bacteria in a room, researchers pumped the air from the room over a Petri dish at the rate of 1 cubic foot per minute for eight carpeted rooms and eight uncarpeted rooms. Colonies of bacteria were allowed to form in the 16 Petri dishes. The results are given in the table below. Assume the distribution to be approximately normal. Do carpeted rooms have more bacteria than uncarpeted rooms? Carpeted Rooms Uncarpeted Rooms 11.7 12.0 8.2 8.3 7.1 3.8 13.1 7.3 10.6 12.0 10.1 11.1 14.8 10.3 14.0 13.7 What is the test statistic for this hypothesis test if group 1 is the carpeted rooms and group 2 is the uncarpeted rooms. 1.43 2.73 0.1831 1.39 0.935Researchers wanted to determine if carpeted rooms contained more bacteria than uncarpeted rooms. To determine the amount of bacteria in a room, researchers pumped the air from the room over a Petri dish at the rate of 1 cubic foot per minute for eight carpeted rooms and eight uncarpeted rooms. Colonies of bacteria were allowed to form in the 16 Petri dishes. The results are given in the table below. Assume the distribution to be approximately normal. Do carpeted rooms have more bacteria than uncarpeted rooms? Carpeted Rooms Uncarpeted Rooms 11.7 12.0 8.2 8.3 7.1 3.8 13.1 7.3 10.6 12.0 10.1 11.1 14.8 10.3 14.0 13.7 What is the critical value(s) for this hypothesis test if group 1 is the carpeted rooms and group 2 is the uncarpeted rooms. 1.895 2.306 2.365 1.833 1.860
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