Skip to main content
Ch. 5 - Normal Probability Distributions
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLarson 8th EditionCh. 5 - Normal Probability DistributionsProblema 5.Q.1b
Capitolo 5, Problema 5.Q.1b

Find each probability using the standard normal distribution.


b. P(z < 2.23)

Guida verificata passo dopo passo
1
Step 1: Understand the problem. The goal is to find the probability that the standard normal variable z is less than 2.23, denoted as P(z < 2.23). The standard normal distribution has a mean of 0 and a standard deviation of 1.
Step 2: Use the standard normal distribution table (z-table) or a statistical software/tool to find the cumulative probability corresponding to z = 2.23. The z-table provides the area under the curve to the left of a given z-value.
Step 3: Locate the row in the z-table corresponding to the first two digits of the z-value (2.2 in this case) and the column corresponding to the second decimal place (0.03 for 2.23).
Step 4: Read the value from the z-table at the intersection of the row and column identified in Step 3. This value represents P(z < 2.23), the cumulative probability.
Step 5: If using statistical software or a calculator, input the z-value (2.23) into the appropriate function (e.g., normalcdf in a graphing calculator or a similar function in software) to directly obtain the cumulative probability.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
3m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Standard Normal Distribution

The standard normal distribution is a special case of the normal distribution where the mean is 0 and the standard deviation is 1. It is represented by the variable 'z', which indicates how many standard deviations an element is from the mean. This distribution is symmetric and bell-shaped, making it essential for calculating probabilities related to normally distributed data.
Video consigliato:
Percorso guidato
09:47
Finding Standard Normal Probabilities using z-Table

Z-Score

A z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. It is calculated by subtracting the mean from the value and then dividing by the standard deviation. In the context of the standard normal distribution, a z-score indicates how far and in what direction a data point deviates from the mean, allowing for the calculation of probabilities.
Video consigliato:
Percorso guidato
06:31
Z-Scores From Given Probability - TI-84 (CE) Calculator

Cumulative Distribution Function (CDF)

The cumulative distribution function (CDF) of a random variable gives the probability that the variable will take a value less than or equal to a specific value. For the standard normal distribution, the CDF can be used to find probabilities like P(z < 2.23) by looking up the z-score in standard normal distribution tables or using statistical software. This function is crucial for determining probabilities in various statistical analyses.
Video consigliato:
Percorso guidato
06:38
Intro to Frequency Distributions
Pratica correlata
Domanda del libro di testo

In a survey of U.S. adults, 81% feel they have little or no control over data collected about them by companies. You randomly select 250 U.S. adults and ask them whether they feel they have control over data collected about them by companies. Use this information in Exercises 11 and 12. (Source: Pew Research Center)


Determine whether you can use a normal distribution to approximate the binomial distribution. If you can, find the mean and standard deviation. If you cannot, explain why.

97
views
Domanda del libro di testo

The random variable x is normally distributed with the given parameters. Find each probability.


c. μ = 5.5, σ ≈ 0.08, P(5.36 < x < 5.64)

101
views
Domanda del libro di testo

The random variable x is normally distributed with the given parameters. Find each probability.


a. μ = 9.2, σ ≈ 1.62, P(x < 5.97)

75
views
Domanda del libro di testo

The random variable x is normally distributed with the given parameters. Find each probability.


d. μ = 18.5, σ ≈ 4.25, P(19.6 < x < 26.1)

139
views
Domanda del libro di testo

The random variable x is normally distributed with the given parameters. Find each probability.


c. μ = 5.5, σ ≈ 0.08, P(5.36 < x < 5.64)

123
views
Domanda del libro di testo

In a standardized IQ test, scores are normally distributed, with a mean score of 100 and a standardized deviation of 15. Use this information in Exercises 3–10. (Adapted from 123test)

What is the highest score that would still place a person in the bottom 10% of the scores?

171
views