For what model are the following expressions the cumulative probability distribution for response? What is the meaning of the 5, ? Pr(Y; 5 j\x)=Pr(4;
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- The population of scores on a nationally standardized test forms a normal distribution with a mean of 300 and a standard deviation of 50. If you take a random sample of n = 25 students, what is the probability that the sample mean will be less than M = 280? Pls explain! Thx!The following table shows the cumulative frequency distribution of time spent on social media per day for a sample of 120 residents in Petaling Jaya. Q3. Time spent (minutes) Cumulative frequency < 34 < 60 < 86 < 112 < 138 < 164 10 80 90 120 (a) Find the value of h, if the mode of this distribution is 77 minutes. (b) Hence, find the mean and median for this distribution. (c) Comment on the distribution.A normal distribution has a mean of u = 50 and 0 = 12 if one score is randomly selected for distribution what is the probability of randomly selectingt a score that is X < 56
- 1 (a) Discuss the two expressions -x;- )² and E(x;- )², both of which are used (n-1) i=1 to measure the spread of a set of observations x1, x2, . .., X. (b) A random sample of n observations is taken from a distribution; the sum of the observations is t, and the sum of the squares of the observations is 12. Explain how to estimate the mean and the variance of the distribution from which the random sample was taken. (c) Given the random sample described in part (b), write down expressions (based on 11 and t2) for estimates of the mean and variance of the mean of a further, independent, random sample of size m , from the original distribution. (d) Given that n = 25, 1, = 400 and t2 = 8800, construct a 99% confidence interval for the mean of the distribution, and use it to test whether or not this mean could be 20.With the usual notations, find the probability of success 'p' for a binomial distribution, if n=6 9 P (X=4) = P(X=2).Suppose that the time spent by children in front of the television set per year has the distribution N(1500, 250) What proportion of children spend less than 1000 hours in front of the television?
- Today, the waves are crashing onto the beach every 5.1 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 5.1 seconds. Round to 4 decimal places where possible. The probability that a person will be born between weeks 18 and 52 is P(18<x<52)P(18<x<52) = The probability that a person will be born after week 40 is P(x > 40) = P(x > 10 | x < 47) =Dandelions have effects on crop production and lawn growth and are studied. In one region, the mean number of dandelions per square meter was found to be 10.8.Find the probability of no dandelions in an area of 1 m².P(X=0)=P(X=0)= Find the probability of at least one dandelion in an area of 1 m².P(at least one) = Find the probability of at most two dandelions in an area of 1 m².P(X≤2)=P(X≤2)=Weights (X) of men in a certain age group have a normal distribution with mean ? = 170 pounds and standard deviation ? = 28 pounds. Find each of the following probabilities. (Round all answers to four decimal places.) (a) P(X ≤ 191) = probability the weight of a randomly selected man is less than or equal to 191 pounds. (b) P(X ≤ 156) = probability the weight of a randomly selected man is less than or equal to 156 pounds. (c) P(X > 156) = probability the weight of a randomly selected man is more than 156 pounds
- The chart to the right shows that a professor's grading distribution is bell shaped, or normally shaped. The mean of the distribution is 74 and the standard deviation is 9. Using a Continuous Variable Normal Bell Distribution Model, calculate the minimum test score needed to score in the top 5% of the class. Complete your work in the worksheet by listing the formula inputs, labels for the formula inputs and make your calculations with formulas. This test problem is similar to what you studied in video # 32, 33 and 34 and homework problems # 17, 21 and 23. Relative Frequency Frequency Professor looks at all test score for a particular test (this is population data), and observes: 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 Mean = 74 Median = 74 Mode = 73 SD=9 0 0 0 up to 10 up 10 to 20 0 20 up to 30 0 30 up to 40 2 40 up to 50 29 50 up to 60 X = Score 112 60 up to 70 225 70 up to 80 111 80 up to 90 21 2 90 up 100 up to 100 to 110For each random variable defined, describe the set of possible values for the variable, and state whether the variable is discrete or continuous. (a) U = number of times a surfer has to paddle in front of a wave before catching one (b) X = length of a randomly selected angelfishWeights (X) of men in a certain age group have a normal distribution with mean μ = 150 pounds and standard deviation σ= 28 pounds. Find each of the following probabilities. (Round all answers to four decimal places.)(a) P(X ≤ 136) = probability the weight of a randomly selected man is less than or equal to 136 pounds.(b) P(X > 136) = probability the weight of a randomly selected man is more than 136 pounds.
