Question

If z is a standard normal variable, find P(Z >0.97). Round to four decimal places. 

A. 0.1660 

B. 0.8340 

C. 0.1922 

D. 0.1685

Answer 1

Answer 2

Concepts and reason

Normal distribution: Normal distribution is a continuous distribution of data that has the bell-shaped curve. The normally distributed random variable x has mean and standard deviation.

Also, the standard normal distribution represents a normal curve with mean 0 and standard deviation 1. Thus, the parameters involved in a normal distribution are mean and standard deviation.

Standardized z-score: The standardized z-score represents the number of standard deviations the data point is away from the mean.

• If the z-score takes positive value when it is above the mean (0).

• If the z-score takes negative value when it is below the mean (0).

Sampling distribution of sample mean:

The sampling distribution of the sample mean for the given sample size n consists of the collection of the means of all possible samples of size n from the population.

Fundamentals

Let , then the standard z-score is found using the formula given below:

Where X denotes the individual raw score, denotes the population mean, and denotes the population standard deviation.

Procedure for finding the probability value from the z-table values is listed below:

1.From the table of standard normal distribution, locate the probability value.

2.Move left until the first column is reached.

3.Move upward until the top row is reached.

4.Locate the probability value, by the intersection of the row and column values gives the area to the left of z.

Or use Excel to get the required values.

The Excel function is, (=NORMSDIST(Z))

Compute

The above probability value can be shown in the plot as follows:

Ans:

The required probability value 0.1660.