Which of the following statements is NOT true about the Central Limit Theorem?
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- The total of the area to the left of zequals=negative 2.31−2.31 and the area to the right of zequals=2.312.31 under the standard normal curve isComplete the following statement by filling in the blank with the appropriate word or phrase. 1. The curve of a normal distribution extends indefinitely at the tail but does not__________. 2. The area under a normal curve is ______. 3. The area under a normal curve may also be expressed in terms of _ or __or___. 4. The measure of the mean, the median and the mode of a normal curve are ___. 5. The skewness of a normal curve is 0 because it is a/an ___________shape. Find the corresponding area between z=0 and each of the following z-values: 1. z =1.75 2. z =-2.58 3. z = 1.32 Determine each of the following areas and show these graphically. Use probability notation in your final answer. 1. At most z = 1.46 2. Between z=-0.78 and z=-1.95 Find each of the following percentile points under the normal curve. Complete your procedures and find the corresponding z-score of each problem. 1. P99 2. P32 Given μ=62 and =8, find the z-score up to two decimal place that corresponds to each…ind the area under the normal curve to the left of zequals=negative 1.54−1.54 plus the area under the normal curve to the right of zequals=2.542.54.
- The total area to the left of zequals=negative 1.02−1.02 and to the right of zequals=1.621.62 under the standard normal curve isThe area between zequals=00 and zequals=3.083.08 under the standard normal curve isSuppose you know that Var(Z)=(k+1)E(Z) where k is 7. Determine the distribution of Z and find its parameter(s), explaining your argument carefully.
- Which of the following statements about the Central Limit Theorem (CLT) is correct?1. The CLT states that the sample mean is always equal to the population mean.2. The CLT states that the sampling distribution of the sample mean is approximately normal for large sample sizes (n > 30).3. The CLT states that the sample mean is equal to the population mean, provided that n > 30.4. The CLT states that the sampling distribution of the population mean is approximately normal, provided that n > 30. In a distribution plot, if the mean is equal to the median, is the possible shape of the distribution skewed to the right, skewed to the left, or symmetric? If batteries have lives that are normally distribute with mean 2, 800 hours and standard deviation 400 hours, using the 68-95-99.7 rule to approximate the percentage of batteries having a life less than 3, 600 hours.ANSWER ONLY 6 TO 8 AND SHOW THE COMPLETE SOLUTION Question Recent studies have shown that Punica granatum (or pomegranate) seeds have germination time that is found to be normally distributed. To verify this, a biologist measured the number of days to germination of 20 random pomegranate seeds. Below shows the data obtained: 15.82 16.69 17.69 18.14 19.38 16.07 16.89 17.98 18.33 19.48 16.49 17.30 18.10 18.50 19.55 16.67 17.67 18.11 19.35 20.66 Using visual inspection with the given histogram and Q-Q Plot below, do the data show evidence that the germination time of pomegranate seeds follows the normal distribution? Explain by interpreting each graph. Figure 1. Histogram Figure 2. Q-Q Plot 2. Using the Wilk-Shapiro Test with R software output given below, do the data show evidence that the germination time of pomegranate seeds follows the normal…What is the Discrete Variable Standard Deviation for the following numbers:x = 0 and P(X = x) = 0.51x = 1 and P(X = x) = 0.11x = 2 and P(X = x) = 0.09x = 3 and P(X = x) = 0.16x = 4 and P(X = x) = 0.13
- The article “Can We Really Walk Straight?” (Amer. J.of Physical Anthropology, 1992: 19–27) reported on anexperiment in which each of 20 healthy men was askedto walk as straight as possible to a target 60 m away atnormal speed. Consider the following observations oncadence (number of strides per second):.95 .85 .92 .95 .93 .86 1.00 .92 .85 .81.78 .93 .93 1.05 .93 1.06 1.06 .96 .81 .96Use the methods developed in this chapter to summarizethe data; include an interpretation or discussion whereverappropriate. [Note: The author of the article used a rathersophisticated statistical analysis to conclude that peoplecannot walk in a straight line and suggested severalexplanations for this.]For each of the following, Circle to indicate whether it is True or False. . True False The standard normal distribution is a normal distribution in which both the mean and standard deviation have a value of 0. True False If either form of test is valid, using a non-parametric test usually gives you more statistical power than analyzing the data with a parametric test. True False The central limit theorem states that the sum (or mean) of a large number of variables will follow a normal distribution. True False When the t-statistic that you calculate from your data is negative and the absolute value is larger than the critical value, then you will reject the null hypothesis.D. Which video streaming platform(s) has(have) the highest median time spent by its patrons? E. Which video streaming platform(s) has(have) the most varied lower 25% of observations? F. Which video streaming platform(s) has(have) at least 75% of its observations less than or equal to 150? G. The upper extreme observation of Disney+ is approximately equal to the upper extreme of which video streaming platform(s)?