Calculate the probability that the sample mean of a variable falls in some range.

At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken What is the probability that the sample mean will be below 0.95 centimeters?

Solution Preview

We have 12 random variables here: X1, X2,... X12 (the 12 observations). These 12 observations are independent random variables: observing a number does not affect the probability distribution of the
subsequent observations (because the sample is a random sample). The sample mean is then another random variable which is obtained by summing the values of X1 through X12 and dividing them by 12:

Mean = (X1+X2+...+X12)/12

We now use ...

Solution Summary

The solution discusses at a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken What is the probability that the sample mean will be below 0.95 centimeters?

... Calculations Z Value -1.959963985 Calculated Sample Size 11.54144961. ... d) Calculate the mean, variance, and standard deviation ... what is the probability that the ...

... week, you will review continuous probabilities, more specifically ...Calculate the correlation coefficient, r, and verify your ... and we're comparing one sample to a ...

... The probability is calculated based on the assumption that ... Type II error is the probability or risk assumed ... _____ 4. In the sample regression equation y = a ...

... a. Calculate the standard error of the mean amount of Medicare spending for a sample of fifty 2003 enrolees ... c. What is the probability the sample mean will ...

... to make judgments of the probability that an ... Although we can calculate these univariate statistics by ... statistics program is capable of calculating them easily ...

... That is the probability calculated using the sample statistic ... interval within which, with some probability, a specified ... What effect does sample size have on ...

...calculator), a handheld graphing calculator, or the ... distribution table, the cumulative probability associated with ... the summary score calculated from subtest ...

... Suppose we wish to calculate seasonal factors and a trend, then calculate the forecasted ... A price index is calculated as: 100 (Pt / P0) for t = 1, 2 ...Probability...

... What % probability is associated with a z-value of 1.3. ... Its very easy to understand and easy to calculate. ... 2. It cannot be calculated for distributions with open ...