Question 1

A random variable X is normally distributed with mean $$\mu = 22.0$$ and standard deviation $$\sigma = 2.4. $$What is the probability that X is between 19.7 and 25.3?

Accepted Answer

$$0.7477$$

Question 2

If Z is a standard normal variable, what is the probability that Z is less than 1.13?

Accepted Answer

$$0.8708$$

Question 3

The probability that Z lies between $$-1.0$$ and $$0.36$$ for a standard normal variable is:

Accepted Answer

$$0.2237$$

Question 4

The lengths of human pregnancies are normally distributed with a mean of $$268$$ days and a standard deviation of $$15$$ days. What is the probability that a pregnancy lasts at least $$300$$ days?

Accepted Answer

$$0.0166$$

Question 5

Assume that women have heights that are normally distributed with a mean of $$63.6$$ inches and a standard deviation of $$2.5$$ inches. Find the value of the quartile $$Q_2.$$

Accepted Answer

$$63.6$$ inches

Question 6

The volumes of soda in quart soda bottles are normally distributed with a mean of $$32.3 oz $$and a standard deviation of $$1.2 oz. $$What percentage of quart soda bottles will have the volume of soda less than $$32 oz$$?

Accepted Answer

$$29.68\%$$

Question 7

Assume that adults have IQ scores that are normally distributed with a mean of $$100$$ and a standard deviation of $$15 (on $$the Wechsler test). Find the IQ score separating the top $$14\%$$ from the others.

Accepted Answer

$$108.4$$

Question 8

What is the probability that the random variable has a value greater than $$3$$?

Accepted Answer

$$0.575$$

Question 9

What is the probability that the random variable has a value between $$4.5$$ and $$7.7$$?

Accepted Answer

$$0.5500$$

Question 10

As the sample size increases, do the sample statistics tend to vary less and be closer to the population parameter?

Accepted Answer

Yes. As the sample size increases, the sample statistics tend to vary less and they tend to be closer to the population parameter.

Question 11

A hospital wants to know the probability that a randomly selected pregnancy lasts less than $$250$$ days. Given the mean is $$268$$ days and standard deviation is $$15$$ days, what is the probability?

Accepted Answer

$$0.0475$$

Question 12

If the probability that Z is less than $$-1.5$$ for a standard normal variable is required, which of the following is correct?

Accepted Answer

$$0.0668$$

Question 13

A manufacturer claims that only $$5\% of $$their soda bottles are underfilled. If the mean volume is $$32.3 oz $$and standard deviation is $$1.2 oz$$, what is the cutoff volume for the lowest $$5\%$$?

Accepted Answer

$$30.75 oz$$

Question 14

If a random variable X is normally distributed, which of the following statements is true?

Accepted Answer

The mean, median, and mode are all equal.

Question 15

A psychologist uses the Wechsler test and wants to know what percentage of adults have IQ scores above $$130. $$The mean is $$100$$ and standard deviation is $$15. $$What is the correct percentage?

Accepted Answer

$$2.28\%$$

Question 16

If the probability that Z is between $$-2$$ and $$2 is $$required, what is the correct value?

Accepted Answer

$$0.9545$$

Question 17

A researcher wants to find the probability that a randomly selected woman is taller than $$68$$ inches. Heights are normally distributed with mean $$63.6$$ inches and standard deviation $$2.5$$ inches.

Accepted Answer

$$0.0228$$

Question 18

If the area under the normal curve to the left of $$z = 1.96 is $$required, what is the correct value?

Accepted Answer

$$0.9750$$

Question 19

A company wants to know the probability that a randomly selected bottle contains more than $$34 oz of $$soda. The mean is $$32.3 oz $$and standard deviation is $$1.2 oz.$$

Accepted Answer

$$0.0475$$

Probability and Normal Distribution: Study Notes for Statistics

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