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If X is normal random variable with mean 3 and variance 5, then find the probability P(2 < X <6).
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- X is a binomial random variable with p = 0.36 For a sample of 25, what is the expected value of X?Let wages denote a person's hourly wages and edu denote their years of education. Suppose that wages = ß1 + Bzedu + ß3edu² + e and that e is normally distributed with mean zero and variance one (so e ~ N(0, 1)). Suppose we know B1 = 1, B2 = 0.2, ß3 = -0.01, and we observe an individual with 16 years of education. What is the probability that her wages are larger than one? In the options below, Z ~ N(0, 1). O a. P(Z > -0.64) Ob. 1- P(Z > 1.64) O c. None of the other options is correct. O d. 1- P(Z > -0.64) O e. P(Z > 1.64)If X is a binomial random variable with n = 15 andp = 0.3, we can use the normal approximation? yes no
- 3. (18/222, Expected Value and Variance) The Philippine Housing Survey reported the following data on the number of bedrooms in owner-occupied and renter-occupied houses in central cities of the country. E(x) = Var (x) = 6x = Bedrooms a. Define a random variable x = number of bedrooms in renter-occupied houses and develop a probability distribution for the random variable. Let x = 4 represent 4 or more bedrooms. Show tabular computation/solution. Compute the expected value, variance, and standard deviation for the number of bedrooms in renter-occupied houses E(y) = 0 1 2 3 4 or more Var (y) = Number of Houses (1,000s) Owner-Occupied 23 541 3,832 8,690 3,783 16,869 Renter-Occupied 547 5,012 6,100 2,644 557 14,860 b. Define a random variable y = number of bedrooms in owner-occupied houses and develop a probability distribution for the random variable. Let y = 4 represent 4 or more bedrooms. Show tabular computation/solution. Compute the expected value, variance, and standard deviation…Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean ? = 62.0 kg and standard deviation ? = 9.0 kg. Suppose a doe that weighs less than 53 kg is considered undernourished. (a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.) (b) If the park has about 2400 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.) (c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 70 does should be more than 59 kg. If the average weight is less than 59 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 70 does is less than 59 kg…Suppose that the random variables X₁,..., X and Y₁,...,Y, are random sample from independent normal distributions N(3,8) and N(3,15), respectively.
- A small manufactured item is produced on an assembly line. Each item either is or not defective; defectives occur independently with probability 0.05. Suppose we start observing items at an arbitrary point on the line. Let X be the number of items we inspect until we find the first defective item. Compute the expected value and variance of X (please justify your answer).Suppose that x is a normally distributed random variable with mean 5and standard distribution is 6. Find z value corresponding to x=17.Total blood volume (in ml) per body weight (in kg) is important in medical research. For healthy adults, the red blood cell volume mean is about µ = 28 ml/kg. Red blood cell volume that is too low or too high can indicate a medical problem. Suppose that Roger has had seven blood tests, and the red blood cell volume sample mean was 32.7 ml/kg. Let x be a random variable that represents Roger’s red blood cell volume. Assume that x has a normal distribution and = 4.75. Do the data indicate that Roger’s red blood cell volume is different (either way) from µ = 28 ml/kg? use a 0.01 level of significance.
- Let X be a random variable with range {20,30,50} and probability distribution P(X=20) = 0.25,P(X=30) = 0.25, and P(X=50) = 0.5. What is the expected value of X?The probability of having a red color ball is 15%. The boy selected four submitted balls at random, let X be a random variable indicating the number of red color balls out of those balls selected by the boy. Identify and compute the expected value for the random variable X, i.e. E(X).Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean ? = 55.0 kg and standard deviation ? = 8.4 kg. Suppose a doe that weighs less than 46 kg is considered undernourished. (a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)(b) If the park has about 2850 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)does(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 40 does should be more than 52 kg. If the average weight is less than 52 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 40 does is less than…
