5. What is the standard deviation for the random variable X? X 0 1 2 3 4 5 P(x) 0.1 0.2 0.1 0.1 0.2 0.3
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- 5. Question from 8.3: Variance and Standard Deviation Find the variance of the probability distribution for the histogram shown. 0.3 0.2 0.1 1 2 3 4 5 XAspirin is packed in 120 tab bottles with weight normally distributed with mean 600g and standard deviation 6g. We want to figure out what is the probabilty that a bottle of aspirin randomly picked from the production batch will weigh from 598g to 602g. 1. Do we have to calculate one z-score or two z-scores? 2. The negative z-score is 3. The positive z-score is 4.The probability that a bottle of aspirin will have weight between 598g and 602g is4. Suppose that the weight of an newborn fawn is Uniformly distributed between 2.3 and 3.9 kg. Suppose that a newborn fawn is randomly selected. Round answers to 4 decimal places when possible. The mean of this distribution is ? The standard deviation is ? The probability that fawn will weigh exactly 3.1 kg is P(x = 3.1) = ? The probability that a newborn fawn will be weigh between 2.8 and 3.8 is P(2.8 < x < 3.8) = ? The probability that a newborn fawn will be weigh more than 3.02 is P(x > 3.02) = ? P(x > 2.5 | x < 3.4) = ? Find the 79th percentile?
- Q1. Researchers developed a "cat IQ test" and find that the population of cats in the United States has a mean score of µ = 25 on this test with a standard deviation of σ = 3. You decide to test a sample of n = 45 cats to do some research about whether some breeds are smarter. What is the expected value of the sampling distribution of the mean?The joint distribution of the pair of random variables as given in the following table: 0 Y 1 2 -10 X 0 10 0.2 0.1 0 0.066 0.046 0.052 0.072 0.042 O No answer 0.1 0.2 0 0.1 0.1 0.2 A random sample of 4 is taken of the random variable X. What is pZX₁/425? (EX//425) ²If X represents a random variable coming from a normal distribution with mean 5 and if P(X>6.1)=0.2, then P(5<X<6.1)=0.3. True False
- h) Probability and Statistics please providea correct and well explained solution for the followingtyWhat is the probability of a male foot length between 10 and 12.5 inches? (Use the same mean of 11 and standard deviation of 1.5 as before.) P(z < 12.5) - P(z < 10) 6 8 10 12 14 16 z = 12.5 1. The mean is u = 11 and the standard deviation, o = 1.5 2. Find the z-score for x = 10. z =| (Round to the nearest hundredth.) 3. Find the z-score for x = 12.5. z = 4. P(10 < x < 12.5) = P( くzく 0.5889 (decimal form) 5. The probability that a male's foot is between 10 and 12.5 inches is 58.89 MacBook O00 E3 F4 F5 F6 F7 * $4 % 3 6
- If x represents a random variable with mean 137 and standard deviation 16, then the standard deviation of the sampling distribution of the means with sample size 64 is 2. True O Falsefind the mean variance and standard deviation25. Each of a random sample of 30 student nurses who participated in a research project was given a test designed to measure the degree of creative thinking. The standard deviation of the scores was 11. Can one conclude from these data that the population variance is less than 400? Let α = 0. 05 and assume that the population is normally distributed. (A) Yes (B) No