Question #6 A random sample of 1026 adults in a certain large country was asked "Do you pretty much think televisions are a necessity or a luxury you could do without?" Of the 1026 adults surveyed, 515 indicated that televisions are a luxury they could do without. Complete parts (a) through (e) below.---**Click here to view the standard normal distribution table (page 1).****Click here to view the standard normal distribution table (page 2).**---**(a)** Obtain a point estimate for the population proportion of adults in the country who believe that televisions are a luxury they could do without.\[\hat{p} = 0.502\](Round to three decimal places as needed.)---**(b)** Verify that the requirements for constructing a confidence interval about p are satisfied.The sample \[\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\] a simple random sample, the value of \[ \_\_\_\_\_] is \[\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_,\] which is \[\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\] 10, and the \[\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\] \[\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\] less than or equal to 5% of the \[\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\].(Round to three decimal places as needed.) ### Understanding the Standard Normal Distribution TableThe standard normal distribution table, often referred to as the Z-table, is crucial in statistics for finding the probability of a statistic falling below, above, or between certain points on a standard normal distribution. The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.#### Page 1##### Diagram OverviewThe diagram on the left side above the table illustrates a normal distribution curve. It highlights the area under the curve to the left of a specific z-value, which represents the cumulative probability. The diagram is labeled with "Area" indicating the portion under the curve and a vertical line depicting the z-value.##### Table Components- **Columns and Rows**: The rows represent z-values ranging from -3.4 to -0.0. The columns labeled 0.00 to 0.09 represent the additional decimal places of the z-values.- **Values**: The values inside the table indicate the cumulative probability from the left up to the given z-value.For example, for z = -2.5 and an additional decimal of 0.03, the cumulative probability is 0.0059.#### Page 2##### Diagram OverviewSimilar to Page 1, this diagram shows the standard normal distribution curve. The shaded area under the curve to the left of a specific positive z-value represents the cumulative probability.##### Table Components- **Columns and Rows**: The rows represent z-values from 0.0 to 3.0. Again, columns 0.00 to 0.09 indicate the decimal extensions of each z-value.- **Values**: The table provides cumulative probabilities corresponding to these z-values.For instance, for z = 1.2 and an additional decimal of 0.05, the cumulative probability is 0.8849.### ApplicationThe Z-table is used to determine probabilities and percentiles for normal distributions, essential for hypothesis testing, confidence interval construction, and other statistical analyses.To use the table, locate the z-value in the leftmost column, move across the row to find the corresponding decimal column, and identify the cumulative probability value.Understanding this table enables statisticians and students to quantify probabilities using the properties of the standard normal distribution, aiding in data-driven decision-making.

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A random sample of 1026 adults in a certain large country was asked "Do you pretty much think televisions are a necessity or a luxury you could do without?" Of the 1026 adults surveyed, 515 indicated that televisions are a luxury they could without. Complete parts (a) through (e) below. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) Obtain a point estimate for the population proportion of adults in the country who believe that televisions are a luxury they could do without. p= 0.502 (Round to three decimal places as needed.) (b) Verify that the requirements for constructing a confidence interval about p are satisfied. The sample a simple random sample, the value of V is , which is V 10, and the V less than or equal to 5% of the (Round to three decimal places as needed.)