Explanation Approach: The bell-shaped normal curve is symmetric with respect to its mean (denoted as μ ). Thus, 50% of the data values lies to the left of mean and remaining 50% of the data lies to the right of the mean. Figure 1 illustrates 68-95-99.7 rule for a normal distribution . Figure 1 Approximately 68% of the data lies between μ − σ and μ + σ , 95% of the data lies between μ − 2 σ and μ + 2 σ , 99.7% of the data lies between μ − 3 σ and μ + 3 σ . Assume a normal distribution has a mean of μ and a standard deviation of σ . We use the equation z = x − μ σ to convert a value x in the nonstandard distribution to a z -score. Given Information: The mean is 30 and the standard deviation is 6. Also, 100 people are there in the group. Calculation: Here, μ = 30 , σ = 6 and x = 20. Substitute μ = 30 , σ = 6 and x = 20 in z = x − μ σ , z = 20 − 30 6 = − 10 6 = − 1.67 Therefore, the corresponding z -score is approximately − 1.67 . That is, P ( x < 20 ) = P ( z < − 1.67 ) . Figure 2 Since the normal distribution curve is symmetric, the area between z = 0 and z = − 1.67 is same as the area between z = 0 and z = 1.67 . To find the area between z = 0 and to a z -score, use the data in the standard normal distribution table. Use the row for z = 1.6 and the column labelled 0.07 in the standard normal distribution table. The data from the standard normal distribution table required for this problem is given below:

6th Edition

ISBN: 9780134434681

Author: Tom Pirnot

Publisher: PEARSON

See similar textbooks

Concept explainers

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of tw…

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency o…

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow compar…

Videos

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 14.4, Problem 68E

To determine

To find:

The number of people who mediate between 20 minutes and 30 minutes per day.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.4, Problem 67E

Chapter 14.4, Problem 69E

Students have asked these similar questions

Module Code: MATH380202 3. (a) Let {} be a white noise process with variance σ2. Define an ARMA(p,q) process {X} in terms of {+} and state (without proof) conditions for {X} to be (i) weakly stationary and (ii) invertible. Define what is meant by an ARIMA (p, d, q) process. Let {Y} be such an ARIMA(p, d, q) process and show how it can also be represented as an ARMA process, giving the AR and MA orders of this representation. (b) The following tables show the first nine sample autocorrelations and partial auto- correlations of X and Y₁ = VX+ for a series of n = 1095 observations. (Notice that the notation in this part has no relationship with the notation in part (a) of this question.) Identify a model for this time series and obtain preliminary estimates for the pa- rameters of your model. X₁ = 15.51, s² = 317.43. k 1 2 3 4 5 6 7 Pk 0.981 0.974 0.968 akk 0.981 0.327 8 9 0.927 0.963 0.957 0.951 0.943 0.935 0.121 0.104 0.000 0.014 -0.067 -0.068 -0.012 Y₁ = VX : y = 0.03, s² = 11.48. k 1…

Let G be a graph with n ≥ 2 vertices x1, x2, . . . , xn, and let A be the adjacency matrixof G. Prove that if G is connected, then every entry in the matrix A^n−1 + A^nis positive.

Module Code: MATH380202 1. (a) Define the terms "strongly stationary" and "weakly stationary". Let {X} be a stochastic process defined for all t € Z. Assuming that {X+} is weakly stationary, define the autocorrelation function (acf) Pk, for lag k. What conditions must a process {X+) satisfy for it to be white noise? (b) Let N(0, 1) for t€ Z, with the {+} being mutually independent. Which of the following processes {X+} are weakly stationary for t> 0? Briefly justify your answers. i. Xt for all > 0. ii. Xo~N(0,) and X₁ = 2X+-1+ &t for t > 0. (c) Provide an expression for estimating the autocovariance function for a sample X1,..., X believed to be from a weakly stationary process. How is the autocor- relation function Pk then estimated, and a correlogram (or acf plot) constructed? (d) Consider the weakly stationary stochastic process ✗+ = + + +-1+ +-2 where {E} is a white noise process with variance 1. Compute the population autocorre- lation function Pk for all k = 0, 1, ....

Chapter 14 Solutions

Mathematics All Around (6th Edition)

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The number of people who mediate between 20 minutes and 30 minutes per day.

Solution Summary: The author illustrates the 68-95-99.7 rule for a normal distribution. The bell-shaped normal curve is symmetric with respect to its mean.

Concept explainers

Videos

To find: The number of people who mediate between 20 minutes and 30 minutes per day.

Want to see the full answer?

Chapter 14 Solutions

To find:

The number of people who mediate between 20 minutes and 30 minutes per day.