A random variable Z is normally distributed with mean and variance are 0 and 1 respectively. Determine the probability of P(1.5
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A: here mean = 46 standard deviation = 5
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Q: Find the variance and standard deviation of X
A: The variance can be calculated as V(X) = E(X2) - [E(X)]2
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- Calculate the expected value, the variance, and standard deviation where X is the number of tails that come up when a coin is tossed three timesAssume the random variable X is normally distributed with mean μ=50 and standard deviation σ=7. Find the 87th percentile.If z is a standard normal variable, find the probability that z is between -2.07 and 3.28
- Write the probability density function of a normal random variable and a standard normal random variable. If the annual rainfall in Cape Town is normally distributed with mean 20.2 inches and standard deviation 3.6 inches. Find the probability that the sum of the next five years’ rainfall exceeds 110 inches.A random variable has a longnormal distribution with mean 10 and variance 4. Calculate the probability that the variable will take a value between 7.5 and 12.5A random sample of size 29 is selected from a normal population with mean = and variance = 8. Determine the probability that s? (the sample variance) is between 11.81 and 14.57. 12
- Service time for a customer coming through a checkout counter in a retail store is a random variable with the mean of 3.0 minutes and standard deviation of 1.5 minutes. Suppose that the distribution of service time is fairly close to a normal distribution. Suppose there are two counters in a store, n¡ = 47 customers in the first line and n2 = 49 customers in the second line. Find the probability that the difference between the mean service time for the shorter line X1 and the mean service time for the longer one X2 is more than 0.6 minutes. Assume that the service times for each customer can be regarded as independent random variables. Round your answer to two decimal places (e.g. 98.76). P = iConsider a random sample from the distribution of Binomial, Poisson, Exponential,Gamma, and normal. Let T4 =∑X /(n + 1). Find the MSE of each statistic and choose the best statistic.When a normal random variable Y is transformed to a standard normal random variable Z, the mean value of Z is 1 and the standard deviation value is 0.
