Let x be a continuous random variable that has a normal distribution with a mean of 50 and a standard deviation of 10. Convert the following x values to z values and find the probabil- ity to the left of these points. (a) x = 55
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- The random variable x has a normal distribution with u = 200 and o = 20. a. Find the probability that x assumes a value more than two standard deviations from its mean. More than three standard deviations from u. b. Find the probability that x assumes a value within one standard deviation of its mean. Within two standard de- viations of c. Find the value of x that represents the 80th percentile of this distribution. The 10th percentile.X is a discrete random variable with the following PMF: • P(X = 5.5) = 0.25 • P(X = -2.5) = 0.25 P(X = 8) = 0.5 Find the standard deviation of X.Disc Brake pads has a Normal distribution with a mean µ = 50,000 miles but with some unknown standard deviation σ . In a sample of n =16 pads is tested for their ‘life-times’ yield S = 2500 as the sample estimate σ . What is the probability that the sample average X16 exceeds 49,000 miles, Pr( 49,000)=_________
- Use the Suppose in a local Kindergarten through 12th grade (K -12) school district, 42% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. nd the mean and the standard deviation of X of B(144, 0.42). Round off to 4 decimal places. b. Now approximate X of B(144, 0.42) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y N( C Find the probability that at most 72 favor a charter school using the normal approximation and the table. Round off to z-values up to 2 decimal places.) P(X 68) P(Y > ~ (Z >) e. Find the probability that exactly 63 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 63) P(Consider a random variable X that follows a normal distribution with a mean (μ) of 50 and a standard deviation (σ) of 5. Calculate the probability that X is less than 40.Find the first two moments about the mean for the random variable X defined by X = -2 with prob. 1/3 3 with prob. 1/2 = 1 with prob. 1/6. %3D
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- Q3: The effective life of a component used in a jet-turbine aircraft engine is a random variable with mean 5000 hours and standard deviation 40 hours. The distribution of effective life is fairly close to a normal component that increases the mean life to 5030 hours and decreases the standard deviation to 30 hours. distribution. The engine manufacturer introduces an improvement into the manufacturing process for this Suppose that a random sample of n₁ = 16 components is selected from the "Old" process and a random sample of n₂ = 25 components is selected from the "Improved" process. What is the probability that difference in the two-sample means that the old and improved processes can be regarded as independent populations. 5 X₂X₁ is at least 15 hours? AssumeFind P(11<X<15) If X is normally distributed with a mean of 14 and a standard deviation of 2?The random variables X is the best described by a normal distribution with = 30 and a = 6. Find the z-score that corresponds to the following X values.:1. X = 212 X = 26.5