TOPIC:Normal distribution.

You are given the following: i) X is a random variable representing size of loss. ii)...
Let X be a random variable with a normal distribution having a mean of 30 and a known standard deviation of 16. What is the probability that X is greater than 50? A- 0.1056 B- 0.6057 C- 0.3944 D- 0.8944
#5 please
2. Find the probability distribution function for the random variable representing picking a random real number between -1 and 1. (This is a piecewise defined function.) 3. Compute the mean of the random variable with density function if x>0 ed f(r) = if r < 0. 0 4. Compute the mean of the random variable with density function 2e (1 - cos x) if x >0 if r<O. f (x) = 5 Compute the variance and standard deviation...
6.33 Let x be a continuous random variable that is normally distributed with a mean of 25 and a standard deviation of 6. Find the probability that x assumes a value a. between 28 and 34 b. between 20 and 35 6.34 Let x be a continuous random variable that has a normal distribution with a mean of 30 and a stan- dard deviation of 2. Find the probability that x assumes a value a. between 29 and 35 b....
Given a random variable X follows a Normal distribution with mean 10 and standard deviation 5, what is the probability that X lies within one standard deviation of the mean?
Question 1 (0.5 points) A random variable X follows a normal distribution with mean of 50 and standard deviation of 5. Suppose we take a simple random sample of size 6 from the population above. Can we calculate the probability that the sample mean is between 45 and 60? (You do not need to actually calculate the probability for this question.) Yes, and the calculated probability would be exact. Yes, and the calculated probability would be approximate. No. Question 2...
1. Given the probability distribution shown for an infinite population with the discrete random variable, x: X: 0 1 2 3 P(X) .2 .05 .3 .45 a. Determine the mean and standard deviation of x. b. For the sample size, n=2, determine the mean for each possible simple random sample from this population. c. For each simple random sample identified in part b, what is the probability that this particular sample will be selected? d. Combining the results of parts...
R studio #Exercise : Calculate the following probabilities : #1. Probability that a normal random variable with mean 22 and variance 25 #(i)lies between 16.2 and 27.5 #(ii) is greater than 29 #(iii) is less than 17 #(iv)is less than 15 or greater than 25 #2.Probability that in 60 tosses of a fair coin the head comes up #(i) 20,25 or 30 times #(ii) less than 20 times #(iii) between 20 and 30 times #3.A random variable X has Poisson...
A random variable having a normal distribution with a mean of 0 and a standard deviation of 1 is said to have a: binomial distribution standard normal probability distribution exponential probability distribution uniform probability distribution
Question 2 (0.5 points) A random variable X follows a normal distribution with mean of 50 and standard deviation of 5. Suppose we take a simple random sample of size 60 from the population above. Can we calculate the probability that the sample mean is between 45 and 60? (You do not need to actually calculate the probability for this question.) Yes, and the calculated probability would be exact. Yes, and the calculated probability would be approximate. No. Question 3...
The random variable X represents the roll of a 10-sided fair die. That is to say its sample space is the set {1,2,3,4,5,6,7,8,9,10}, with each outcome equally likely. Calculate the following population parameters: a.) The population mean: μx = _______ b.) The population variance and standard deviation: c.) The expected value E[X²] 9.) For the normal random variable X with mean μ = 50 and standard deviation σ = 4, a.) Find the probability P(x > 60) = b.) Find the probability (49 < x̄ <...