You calculated Normal Distribution Probability using these numbers:where X is less than 67.59 for a mean of 65, and standard deviation of 12.35

What is the probability that a normally distributed random variable lies within 1.65 standard deviations of the mean?Note: You can use the Z table here.95%90%85%80%

Normal VariablesWhat is the probability of a normally distributed random variable lying within 1.65 standard deviations of the mean?

Suppose a normal distribution has a mean of 79 and a standard deviation of 7. What is P(x ≥ 93)?A.0.025B.0.16C.0.84D.0.975SUBMITarrow_backPREVIOUS

You have taken a random sample of size =n80 from a normal population that has a population mean of =μ60 and a population standard deviation of =σ16. Your sample, which is Sample 1 in the table below, has a mean of =x62.7. (In the table, Sample 1 is written "S1", Sample 2 is written "S2", etc.)(a)Based on Sample 1, graph the 75% and 95% confidence intervals for the population mean. Use 1.150 for the critical value for the 75% confidence interval, and use 1.960 for the critical value for the 95% confidence interval. (If necessary, consult a list of formulas.)Enter the lower and upper limits on the graphs to show each confidence interval. Write your answers with one decimal place.For the points ( and ), enter the population mean, =μ60.75% confidence interval51.068.0 95% confidence interval51.068.0(b)Press the "Generate Samples" button below to simulate taking 19 more samples of size =n80 from the population. Notice that the confidence intervals for these samples are drawn automatically. Then complete parts (c) and (d) below the table.x 75%lowerlimit 75%upperlimit 95%lowerlimit 95%upperlimitS1 62.7 ? ? ? ?S2 58.9 56.8 61.0 55.4 62.4S3 61.1 59.0 63.2 57.6 64.6S4 58.9 56.8 61.0 55.4 62.4S5 61.3 59.2 63.4 57.8 64.8S6 64.1 62.0 66.2 60.6 67.6S7 57.1 55.0 59.2 53.6 60.6S8 57.2 55.1 59.3 53.7 60.7S9 59.9 57.8 62.0 56.4 63.4S10 60.3 58.2 62.4 56.8 63.8S11 64.2 62.1 66.3 60.7 67.7S12 61.1 59.0 63.2 57.6 64.6S13 59.3 57.2 61.4 55.8 62.8S14 61.2 59.1 63.3 57.7 64.7S15 58.5 56.4 60.6 55.0 62.0S16 60.5 58.4 62.6 57.0 64.0S17 62.8 60.7 64.9 59.3 66.3S18 57.1 55.0 59.2 53.6 60.6S19 59.8 57.7 61.9 56.3 63.3S20 60.7 58.6 62.8 57.2 64.275% confidence intervals51.068.095% confidence intervals51.068.0(c)Notice that for =182090% of the samples, the 95% confidence interval contains the population mean. Choose the correct statement. When constructing 95% confidence intervals for 20 samples of the same size from the population, exactly 95% of the samples must contain the population mean. There must have been an error with the way our samples were chosen. When constructing 95% confidence intervals for 20 samples of the same size from the population, the percentage of the samples that contain the population mean should be close to 95%, but it may not be exactly 95%. When constructing 95% confidence intervals for 20 samples of the same size from the population, at most 95% of the samples will contain the population mean.(d)Choose ALL that are true. The 75% confidence interval for Sample 5 indicates that 75% of the Sample 5 data values are between 59.2 and 63.4. From the 95% confidence interval for Sample 5, we cannot say that there is a 95% probability that the population mean is between 57.8 and 64.8. The 75% confidence interval for Sample 5 is narrower than the 95% confidence interval for Sample 5. This must be the case, because when a confidence interval is constructed for a sample, the greater the level of confidence, the wider the confidence interval. If there were a Sample 21 of size =n160 taken from the same population as Sample 5, then the 95% confidence interval for Sample 21 would be wider than the 95% confidence interval for Sample 5. None of the choices above are true.CheckSave For LaterSubmit Assignment

Suppose a normal distribution has a mean of 62 and a standard deviation of 4. What is the probability that a data value is between 57 and 65? Round your answer to the nearest tenth of a percent.A.69.8%B.67.8%C.68.8%D.66.8%SUBMITarrow_backPREVIOUS