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Exam 6: The Normal Distribution

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Question 41

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$\text { Find the } z \text {-score for which the area to the left is } 0.13 \text {. }$

A) -1.40
B) -1.01
C) -1.13
D) -0.87

E) A) and B)
F) B) and D)

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Question 42

Multiple Choice

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$\text { Find the } z \text { value that corresponds to the given area. }$

A) -0.51
B) 1.33
C) 0.41
D) -0.22

E) All of the above
F) A) and B)

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Question 43

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Identify the type of distribution pattern that occurs when the majority of the data values fall to the left of the mean?

A bottler of drinking water fills plastic bottles with a mean volume of 1001 milliliters (mL) and standard deviation 6 mL. The fill volumes are normally distributed. What Proportion of bottles have volumes less than 1001 mL?

Which of the following characteristics does not apply to a theoretical normal distribution?

The following formula can be used to find the specific value of the variable in a data set t. corresponds to a particular value of the standard normal variable: $X = z \cdot \sigma + \mu$

$\text { Find the area under the standard normal curve to the left of } z = 1.5 \text {. }$

A(n) is employed when a continuous distribution is used to approximate a discrete distribution.

$X$ is a normally distributed random variable with a mean of 10 and a standard deviation of $4.0$ . Find the value of $X$ for which $70.54 \%$ of the area under the distribution curve lies right of it. (Note: the diagram is not necessarily to scale.)

A sample of size 45 will be drawn from a population with mean 10 and standard deviation 5 . Find the probability that $\bar { x }$ will be greater than 11 .

To find the area under the standard normal distribution curve between two $z$ values, one first finds the difference between the two $z$ values, then locates the value corresponding to that difference in the Standard Normal Distribution table.

A(n) is a distribution of means obtained from samples of a specific size taken from a population.

A contractor decided to build homes that will include the middle 80% of the market. If the average size of homes built is 2010 square feet, find the maximum and minimum Sizes of the homes the contractor should build. Assume that the standard deviation is 90 Square feet and the variable is normally distributed.

Use the normal approximation to the binomial to find that probability for the specific value of $X$ . $n = 30 , p = 0.4 , X = 5$

A gardener buys a package of seeds. Seventy-nine percent of seeds of this type germinate. The gardener plants 110 seeds. Approximate the probability that 84 or more Seeds germinate.

A bottler of drinking water fills plastic bottles with a mean volume of 998 milliliters (mL) and standard deviation 7 mL. The fill volumes are normally distributed. What Proportion of bottles have volumes greater than 999 mL?

$\text { Find the area under the standard normal curve that lies between } z = - 1.9 \text { and } z = 2.2 \text {. }$

The area under a normal distribution curve is always positive even if the $z$ value is negative.

Use the normal approximation to find the indicated probability. The sample size is population proportion of successes is $p$ , and $X$ is the number of successes in the sample. $n = 90 , p = 0.6 : P ( X \geq 63 )$

If a baseball player's batting average is 0.340 (i.e., the probability of getting a hit each time at bat is 0.340) , find the probability that the player will have a bad season and get at Most 60 hits in 200 times at bat?