Table of contents

1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 22m
11. Correlation1h 6m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
14. ANOVA1h 0m

6. Normal Distribution and Continuous Random Variables

Standard Normal Distribution

Statistics

6. Normal Distribution and Continuous Random Variables

Standard Normal Distribution

Previous problemNext problem

1:21 minutes

Problem 5.RE.8

Textbook Question

In Exercises 7–18, find the indicated area under the standard normal curve. If convenient, use technology to find the area.

To the left of z = -1.95

Verified step by step guidance

Step 1: Understand the problem. You are tasked with finding the area under the standard normal curve to the left of z = -1.95. This represents the cumulative probability for a z-score of -1.95 in a standard normal distribution.

Step 2: Recall that the standard normal distribution is symmetric about the mean (z = 0), and the total area under the curve is 1. The area to the left of a given z-score represents the cumulative probability up to that z-score.

Step 3: Use the z-score table (also called the standard normal table) or technology (such as a graphing calculator or statistical software) to find the cumulative probability corresponding to z = -1.95. The table or software will provide the area to the left of this z-score.

Step 4: If using a z-score table, locate the row corresponding to -1.9 and the column corresponding to 0.05 (since -1.95 = -1.9 + 0.05). The intersection of this row and column gives the cumulative probability.

Step 5: If using technology, input the z-score of -1.95 into the appropriate function (e.g., 'normalcdf' on a calculator or a similar function in statistical software) to directly obtain the cumulative probability. This value represents the area under the curve to the left of z = -1.95.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Standard Normal Distribution

The standard normal distribution is a special normal distribution with a mean of 0 and a standard deviation of 1. It is used to describe how data points are distributed in a standardized way, allowing for comparison across different datasets. The area under the curve represents probabilities, with the total area equaling 1.

Z-scores

A Z-score indicates how many standard deviations a data point is from the mean of a distribution. It is calculated by subtracting the mean from the data point and dividing by the standard deviation. In the context of the standard normal distribution, a Z-score of -1.95 means the value is 1.95 standard deviations below the mean.

Area Under the Curve

The area under the curve of a probability distribution represents the likelihood of a random variable falling within a particular range. For the standard normal distribution, this area can be found using Z-tables or technology, such as statistical software, to determine probabilities associated with specific Z-scores.

Watch next

Master Finding Standard Normal Probabilities using z-Table with a bite sized video explanation from Patrick

Start learning

Related Videos

Related Practice

Textbook Question

In Exercises 21–26, find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability.

P(z < 1.28)

views

Textbook Question

In Exercises 7–18, find the indicated area under the standard normal curve. If convenient, use technology to find the area.

To the left of z = -1.5 and to the right of z = 1.5

views

Textbook Question

In Exercises 7–18, find the indicated area under the standard normal curve. If convenient, use technology to find the area.

Between z = -1.55 and z = 1.04

views

Textbook Question

In Exercises 7–18, find the indicated area under the standard normal curve. If convenient, use technology to find the area.

To the left of z = -2.825

views

Textbook Question

In Exercises 5 and 6, find the area of the indicated region under the standard normal curve. If convenient, use technology to find the area.

views

Textbook Question

In Exercises 1 and 2, use the normal curve to estimate the mean and standard deviation.

views

Textbook Question

Employee Wellness A survey of employed U.S. adults found that only 35% believe their employer cares about their well-being. You randomly select a sample of U.S. employees. Find the probability that fewer than 100 believe their employer cares about their well-being. (Source: Gallup)

c. You select 400 U.S. employees.

views

Textbook Question

Daily Commute About 83% of U.S. employees drive their own vehicle to work. You randomly select a sample of U.S. employees. Find the probability that more than 100 of the employees drive their own vehicle to work. (Source: U.S. Bureau of Labor Statistics)

c. You select 150 U.S. employees.

views

Show more practices

Download the Mobile app

Privacy

Do not sell my personal information

Accessibility

Patent notice

Sitemap

In Exercises 7–18, find the indicated area under the standard normal curve. If convenient, use technology to find the area.To the left of z = -1.95

Key Concepts

Standard Normal Distribution

Z-scores

Area Under the Curve

Watch next

In Exercises 7–18, find the indicated area under the standard normal curve. If convenient, use technology to find the area.

To the left of z = -1.95