Concept explainers
To graph Problems 59-62, use a graphing calculator and refer to the normal
Graph equation (1) with
(A)
(B)
Graph both in the same viewing window with
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- What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?arrow_forwardProblem#3: The number of messages sent per hour over a computer network has the following distribution: x = number of messages 10 11 12 13 14 15 f(x) 0.08 0.15 0.30 0.20 0.20 0.07 Determine the mean and standard deviation of the number of messages sent per hour.arrow_forwardA sample of n = 15 scores ranges from a high of X = 11 to a low of X = 3. If these scores are placed in a frequency distribution table, how many X values will be listed in the first column?arrow_forward
- Question 2. Many older homes have electrical systems that use fuses rather than circuit breakers. A manufacturer of 40-amp fuses wants to make sure that the mean amperage at which its fuses burn out is in fact 40, i.e., u = 40. If the mean amperage is lower than 40, customers will complain because the fuses require replacement too often. If the mean amperage is higher than 40, the manufacturer might be liable for damage to an electrical system due to fuse malfunction. (a) To verify the amperage of the fuses, a random sample of fuses is to be selected and inspected. If a hypothesis test were to be performed on the resulting data, what null and alternative hypotheses would be of interest to the manufacturer? Ho = 40 versus Ha > 40 fl Hoμ = 40 versus Ha: μ 40 versus Ha : μ < 40 49 49 (b) Suppose a random sample of size n = 49 is taken, and it is given that 2₁ Xi = 2058 and ₁x² = 87250.77. Test the hypothesis you selected in (a) against its alternative at the significance level a = 0.05.…arrow_forwardFor data that is not normally distributed we can't use z-scores. However, there is an equation that works on any distribution. It's called Chebyshev's formula. The formula is where P=1- 1/k2 p is the minimum percentage of scores that fall within kk standard deviations on both sides of the mean. Use this formula to answer the following questions. b) If you have scores that are normally distributed, find the percentage of scores that fall within 3.3 standard deviations on both sides of the mean? c) If you have scores and you don't know if they are normally distributed, how many standard deviations on both sides of the mean do we need to go to have 35 percent of the scores? Note: To answer part c you will need to solve the equation for k.k. A manufacturer knows that their items have a normally distributed length, with a mean of 5.3 inches, and standard deviation of 1.5 inches.If one item is chosen at random, what is the probability that it is less than 8.3 inches long?arrow_forwardQ. 2 Suppose we followed a population of 175 persons for one year, and 50 had a disease of interest at the start of follow-up and another 25 new cases developed during the year. (a) What is the period prevalence for the year? (b) What is the point prevalence at the start of the period? (c) What is the cumulative incidence for the one-year period?arrow_forward
- Two geysers that are near to each other are labelled as Geyser A and Geyser B. The time between eruptions for a given geyser follows an exponential distribution. The eruption times of the two geysers are independent of one another. The mean amount of time between eruptions of Geyser A is 39 minutes, and the mean amount of time between eruptions of Geyser B is 66 minutes. Given that exactly one of the geysers erupts within the next 49 minutes, determine the probability that it will be Geyser A. O 0.6654 0.7850 O 0.7252 O 0.6953 O 0.7551arrow_forwardA scientist is interested in two different types of particles; type A and type B. The time that it takes for a particle of type A to decay can be modeled as an exponential distribution with a mean of 75 minutes, and the time that it takes for a particle of type B to decay can be modeled as an exponential distribution with a mean of 50 minutes. Suppose that a container holds 10 particles; 7 of type A and 3 of type B. Assume that the rate at which each of the particles decays is independent of all of the other particles in the container. (1) Calculate the probability that the first particle to decay is of type A. (2) Calculate the probability of the following event; "it takes at least 30 minutes for any of the particles to decay, and the first particle that decays is of type B".arrow_forwardWhat is the Discrete Variable Standard Deviation for the following numbers:x = 0 and P(X = x) = 0.51x = 1 and P(X = x) = 0.11x = 2 and P(X = x) = 0.09x = 3 and P(X = x) = 0.16x = 4 and P(X = x) = 0.13arrow_forward
- 2. Problem 2: In a population, the correlation coefficient between weight and adiposity is 0.9. The mean weight is 150 lb. The standard deviation in weight is 30 lb. Adiposity is measured on a scale such that the mean is 0.8, and the standard deviation is 0.1. (a) Using this information, predict the expected adiposity of a subject whose weight is 170 lb (b) Using this information, predict the expected weight of a subject whose adiposity is 0.75arrow_forwardProblem 7 A mall is promoting an event of sales. Every $10 a customer spends can get a fortune ticket. Each ticket has a chance of 0.08 to win a gift. How much should a customer spend, so that the probability of getting at least one gift is 0.95. Perform our calculation use normal approximation with continuous correction.arrow_forwardWhat percentage of all possible observations of the variable lie between 1/4 and 5/8arrow_forward