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Find the indicated z-score. Be sure to draw a standard normal curve that depicts the solution. Find the \(z\) -score such that the area under the standard normal curve to its right is \(0.35 .\)

The reaction time \(X\) (in minutes) of a certain chemical process follows a uniform probability distribution with \(5 \leq X \leq 10 .\) (a) Draw the graph of the density curve. (b) What is the probability that the reaction time is between 6 and 8 minutes? (c) What is the probability that the reaction time is between 5 and 8 minutes? (d) What is the probability that the reaction time is less than 6 minutes?

Compute \(P(x)\) using the binomial probability formula. Then determine whether the normal distribution can be used as an approximation for the binomial distribution. If so, approximate \(P(x)\) and compare the result to the exact probability. $$ n=85, p=0.8, x=70 $$

In a recent poll, the Gallup Organization found that \(45 \%\) of adult Americans believe that the overall state of moral values in the United States is poor. Suppose a survey of a random sample of 500 adult Americans is conducted in which they are asked to disclose their feelings on the overall state of moral values in the United States. Use the normal approximation to the binomial to approximate the probability that (a) exactly 250 of those surveyed feel the state of morals is poor. (b) no more than 220 of those surveyed feel the state of morals is poor. (c) more than 250 of those surveyed feel the state of morals is poor. (d) between 220 and 250 , inclusive, believe the state of morals is poor. (e) at least 260 adult Americans believe the overall state of moral values is poor. Would you find this result unusual? Why?

According to a study done by Nick Wilson of Otago University Wellington, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and observe 300 randomly selected individuals' habits as they sneeze. Use the normal approximation to the binomial to approximate the probability that of the 300 randomly observed individuals: (a) exactly 100 do not cover the mouth when sneezing. (b) fewer than 75 do not cover the mouth. (c) Would you be surprised if, after observing 300 individuals, more than 100 did not cover the mouth when sneezing? Why?

Draw a normal curve and label the mean and inflection points. $$ \mu=30 \text { and } \sigma=10 $$

Draw a normal curve and label the mean and inflection points. $$ \mu=50 \text { and } \sigma=5 $$

Assume that the random variable \(X\) is normally distributed, with mean \(\mu=50\) and standard deviation \(\sigma=7 .\) Compute the following probabilities. Be sure to draw a normal curve with the area corresponding to the probability shaded. \(P(38

Monthly charges for cell phone plans in the United States are normally distributed with mean \(\mu=\$ 62\) and standard deviation \(\sigma=\$ 18 .\) (a) Draw a normal curve with the parameters labeled. (b) Shade the region that represents the proportion of plans that charge less than \(\$ 44\) (c) Suppose the area under the normal curve to the left of \(x=\$ 44\) is 0.1587 . Provide two interpretations of this result.

The lives of refrigerators are normally distributed with mean \(\mu=14\) years and standard deviation \(\sigma=2.5\) years Source: Based on information from Consumer Reports (a) Draw a normal curve with the parameters labeled. (b) Shade the region that represents the proportion of refrigerators that last for more than 17 years. (c) Suppose the area under the normal curve to the right of \(x=17\) is 0.1151 . Provide two interpretations of this result.