Decide which of the following statements are true. -Normal distributions are bell-shaped, but they do not have to be symmetric. -The line of symmetry for all normal distributions is x = 0. -On any normal distribution curve, you can find data values more than 5 standard deviations above the mean. -The x-axis is a horizontal asymptote for all normal distributions.

Question
Normal distributions
asked 2020-12-15
Decide which of the following statements are true.
-Normal distributions are bell-shaped, but they do not have to be symmetric.
-The line of symmetry for all normal distributions is x = 0.
-On any normal distribution curve, you can find data values more than 5 standard deviations above the mean.
-The x-axis is a horizontal asymptote for all normal distributions.

Answers (1)

2020-12-16
Step 1
The normal curves approaches to or for x that is the x axis is the horizontal asymptote for the normal distribution.
Thus, the statement 'The x axis is the horizontal asymptote for all the normal distribution' is true.
Step 2
Correct answer:
The x axis is the horizontal asymptote for all the normal distribution
0

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Indicate true or false for the following statements. If false, specify what change will make the statement true.
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d) The standard normal (z) score may be used for inferences concerning population proportions.
e) The F distribution is symmetric and has a mean of 0.
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g) It is not necessary to have equal sample sizes for the paired t test.
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A new thermostat has been engineered for the frozen food cases in large supermarkets. Both the old and new thermostats hold temperatures at an average of \(25^{\circ}F\). However, it is hoped that the new thermostat might be more dependable in the sense that it will hold temperatures closer to \(25^{\circ}F\). One frozen food case was equipped with the new thermostat, and a random sample of 21 temperature readings gave a sample variance of 5.1. Another similar frozen food case was equipped with the old thermostat, and a random sample of 19 temperature readings gave a sample variance of 12.8. Test the claim that the population variance of the old thermostat temperature readings is larger than that for the new thermostat. Use a \(5\%\) level of significance. How could your test conclusion relate to the question regarding the dependability of the temperature readings? (Let population 1 refer to data from the old thermostat.)
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What are the degrees of freedom?
\(df_{N} = ?\)
\(df_{D} = ?\)
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The populations follow independent normal distributions. We have random samples from each population.The populations follow dependent normal distributions. We have random samples from each population.The populations follow independent normal distributions.The populations follow independent chi-square distributions. We have random samples from each population.
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Identify the null and alternative hypothesis in the following scenario.
To determine if battery 1 lasts longer than battery 2, the mean lasting times, of the two competing batteries are compared. Twenty batteries of each type are randomly sampled and tested. Both populations have normal distributions with unknown standard deviations.
Select the correct answer below: \(H_{0}:\mu_{1}\geq\mu_{2}, H_{a}:\mu_{1}<\mu_{2}\)
\(H_{0}:\mu_{1}\leq −\mu_{2}, H_{a}:\mu_{1}>−\mu_{2}\)
\(H_{0}:\mu_{1}\geq −\mu_{2}, H_{a}:\mu_{1}<−\mu_{2}\)
\(H_{0}:\mu_{1}=\mu_{2}, H_{a}:\mu_{1}\neq \mu_{2}\)
\(H_{0}:\mu_{1}\leq \mu_{2}, H_{a}:\mu_{1}>\mu_{2}\)
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a) Which of the following properties distinguishes the standard normal distribution from other normal distributions?
-The mean is located at the center of the distribution.
-The total area under the curve is equal to 1.00.
-The curve is continuous.
-The mean is 0 and the standard deviation is 1.
b) Find the probability \(\displaystyle{P}{\left({z}{<}-{0.51}\right)}\) using the standard normal distribution.
c) Find the probability \(\displaystyle{P}{\left({z}{>}-{0.59}\right)}\) using the standard normal distribution.
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