1. A random variable is known to be normally distributed with the parameters shown below. Complete...

1. A random variable is known to be normally distributed with the parameters shown below. Complete parts a and b.

μ=8.1and σ equals=0.70

a. Determine the value of x such that the probability of a value from this distribution exceeding x is at most 0.05.

b. Referring to your answer in part a, what must the population mean be changed to if the probability of exceeding the value of x found in part a is reduced from 0.20 to 0.10?

2. A randomly selected value from a normal distribution is found to be 1.7 standard deviations above its mean.

a. What is the probability that a randomly selected value from the distribution will be greater than 1.7 standard deviations above the mean?

b. What is the probability that a randomly selected value from the distribution will be less than 1.7 standard deviations from the mean?

3. Assume that a random variable is normally distributed with a mean of 1,500 and a variance of 387.

a. What is the probability that a randomly selected value will be greater than 1563?

4. A random variable is normally distributed with a mean of 45 and a standard deviation of 55. If an observation is randomly selected from the distribution,

a. What value will be exceeded 10% of the time?

b. What value will be exceeded 80% of the time?

c. Determine two values of which the smaller has 15% of the values below it and the larger has 15% of the values above it.

d. What value will 20% of the observations be below?

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orchestra answered 1 year ago

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