Probabilities and areas under a curve Discuss why probabilities for the normal distribution and other continuous...

Probabilities and areas under a curve

Discuss why probabilities for the normal distribution and other continuous distributions are the same as areas under the curve for a given interval.

Expert Solution

orchestra answered 1 year ago

1.) Find the following areas under the standard normal curve.

1.) Find the following areas under the standard normal curve. a. The area to the left of z = -0.76 b. The area to the right of z = -1.36 c. The area between z = -1.22 and z = 1.33 2.) A large group of students took a test in Finite Math where the grades had a mean of 75 and a standard deviation of 4. Assume that the distribution of these grades is approximated by a normal...

In a normal distribution curve, what percentage of the area under the curve is contained in...

In a normal distribution curve, what percentage of the area under the curve is contained in the region, on one side of the mean, between 1 standard deviation from the mean and 2 standard deviations from the mean? A. 95% B. 68.27% C. 50% D. 27.24%% E. 13.59%

- What is a normal distribution and why is it useful for understanding probabilities and statistics?...

- What is a normal distribution and why is it useful for understanding probabilities and statistics? Provide an example of a normal distribution and explain why it can be categorized as a normal distribution. - What is the difference between a standard normal distribution and a normal distribution? - How do we standardize a normal distribution? - What is a z-score? How do we calculate the z-score for a normal variable? - How could the standard normal (z) distribution table...

The normal distribution or bell-shaped curve from statistics provides an example of a continuous probability distribution...

The normal distribution or bell-shaped curve from statistics provides an example of a continuous probability distribution curve. While calculating the probability of the occurrence of an event, we find that the area under the curve between the desired range of profitability values is 0.438. What does this mean? A. The probability of the occurrence of the event is 56.2 percent. B. The probability of the occurrence of the event is 0.438 percent. C. The probability of the occurrence of the...

Find the area under the curve of the normal distribution that is in the following interval:...

Find the area under the curve of the normal distribution that is in the following interval: -2.95 < Z < -2.00 Enter this answer as a number rounded to four digits after the decimal point. Do not use words.

About % of the area under the curve of the standard normal distribution is outside the...

About % of the area under the curve of the standard normal distribution is outside the interval z=[−1.42,1.42]z=[-1.42,1.42] (or beyond 1.42 standard deviations of the mean).

a. About % of the area under the curve of the standard normal distribution is outside...

a. About % of the area under the curve of the standard normal distribution is outside the interval z=[−0.3,0.3]z=[-0.3,0.3] (or beyond 0.3 standard deviations of the mean). b. Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(−b<z<b)=0.6404P(-b<z<b)=0.6404, find b. b= c. Suppose your manager indicates that for a normally distributed data set you are analyzing, your company wants data points between z=−1.6z=-1.6 and z=1.6z=1.6 standard deviations of the mean (or...

Normal probability distribution Is a continuous distribution Review the in-class Excel worksheet and list criteria under...

Normal probability distribution Is a continuous distribution Review the in-class Excel worksheet and list criteria under which it is appropriate to use the normal distribution in the calculation of probabilities Review the Excel Normal Distribution video clip in the In-class Excel folder. The feature needs the mean and the standard deviation of the distribution under study. Use Excel to calculate the following Normal distribution probabilities: Mean = 5ft, standard deviation = .7ft. The probability that a woman’s height is over...

In finding the areas under the normal curve, if we wish to determine the area above...

In finding the areas under the normal curve, if we wish to determine the area above A, and A is greater than the mean, we? A) we find the area below A on the positive Z table and subtract it from .5000 . B) we find the area below A on the positive Z table and subtract it from 1.000. C) the positive Z table gives us the area above A D) we find the area below A on the...

Find the indicated area under the curve of the standard normal distribution; then convert it to...

Find the indicated area under the curve of the standard normal distribution; then convert it to a percentage and fill in the blank. About ________% of the area is between z = -3.5 and z = 3.5 (or within 3.5 standard deviations of the mean).

Question