Solve using coding in R script: 1) Given a standard normal distribution, find the value of...

Solve using coding in R script:

1) Given a standard normal distribution, find the value of k such that P(Z < k) = 0.0197.

2) Given a normal distribution with mu = E(X) = 32 and sigma^2 = V(X) = 30, find the normal curve area to the left of x = 31. Report your code as well as your final answer (4 decimals).

3) A company pays its employees an average wage of $17.90 an hour with a standard deviation of $1.50. If the wages are approximately normally distributed and paid to the nearest cent, the highest 2.5% of the employees hourly wages is greater than what amount?

4) Review question: Let X be a Binomial Random Variable with 8 trials and a probability of success as 0.37. Suppose you want to find k such that P(X < k) = 0.6625. What is the value of k?

Expert Solution

orchestra answered 1 year ago

Using the z table (The Standard Normal Distribution Table), find the critical value (or values) for...

Using the z table (The Standard Normal Distribution Table), find the critical value (or values) for the two-tailed test with a=0.05 . Round to two decimal places, and enter the answers separated by a comma if needed.

to find a probability of values in a tail of the normal distribution using a standard...

to find a probability of values in a tail of the normal distribution using a standard normal table

Find the following percentile for the standard normal distribution. Draw a sketch and show the R...

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Find the probability for Z>-0.97 given that Z is Standard Normal Distribution?

Find the probability for Z<1.14 given that Z is Standard Normal Distribution?

Given a standard normal distribution, find the area under the curve that lies (a) to the...

Given a standard normal distribution, find the area under the curve that lies (a) to the right of z=1.25; (b) to the left of z= -0.4; (c) to the left of z= 0.8; (d) between z=0.4 and z=1.3; (e) between z= -0.3 and z= 0.9; and (f) outside z= -1.5 to z= 1.5.

For the standard normal distribution, find the value of c such that: P(z > c) =...

For the standard normal distribution, find the value of c such that: P(z > c) = 0.0025

Coding Language: R Generate 100 observations from the normal distribution with mean 3 and variance 1....

Coding Language: R Generate 100 observations from the normal distribution with mean 3 and variance 1. Compute the sample average, the standard error for the sample average, and the 95% confidence interval. Repeat the above two steps 1000 times. Report (a) the mean of the 1000 sample means, (b) the standard deviation of the 1000 sample means, (c) the mean of the 1000 standard errors, and (d) how many times (out of 1000) the 95% confidence intervals include the population...

Find the indicated probability using the standard normal distribution. P(z < -0.39)

1. Suppose a random variable, Z, follows a Standard Normal distribution. Find the following probabilities using...

1. Suppose a random variable, Z, follows a Standard Normal distribution. Find the following probabilities using the z-table. For the Z distribution, find the following. Use z-table and check with Excel. Sketch, etc. (a) the 28th percentile (b) the 59th percentile.

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