STATS CH.7

7. If x is the mean of a large (n > 30) simple random sample from a population with mean μ and standard deviation σ, then x is approximately normal with ox = o/sqrt(n).

True

16. If a normal population has a mean of μ and a standard deviation of σ, then P (X = μ) = 0.

True?

12. A z-score indicates how many standard deviations a value is above or below the mean.

True??

11. The area under the entire probability density curve is equal to __________.

1

13. If a normal population has a mean of μ and a standard deviation of σ, then the area to the left of μ is less than 0.5.

False

15. If a normal population has a mean of μ and a standard deviation of σ, then P (X = μ) = 1.

False

18. The area under the normal curve to the left of the mode is less than 0.5.

False

8. If X is a binomial random variable with n trials and success probability p, then as n gets larger, the distribution of X becomes more skewed.

False?

14. Points on the horizontal axis to the left of the mode have __________ z-scores.

Negative

11. Z-scores follow a standard normal distribution.

True

14. If a normal population has a mean of μ and a standard deviation of σ, then the area to the right of μ + σ is less than 0.5.

True

6. The __________ states that the sampling distribution of x is approximately normal when the sample is large.

central limit theorem

6. The adjustment made when approximating a discrete random distribution with a continuous one is called the __________ correction.

continuity

9. The proportion of a population that is contained within an interval corresponds to an area under the probability __________ curve.

density

8. If n is the sample size, p is the population proportion, and p^ is the sample proportion, then o = np

False; o = sqrt(p(1-p)/n)

17. A normal curve is wide and flat when the standard deviation is small.

False; when sd is large

5. If X is a binomial random variable and if np ≥ 10 and n(1 −p) ≥ 10, then X is approximately normal with μX = __________ and σX = __________.

np sqrt(np(1-p))

7. A population is rejected as being approximately normal if the sample contains an __________, if the sample contains a large degree of _________, or if the sample has more than one distinct __________.

outlier, skewness, mode

5. If n is the sample size and x is the number in the sample who have a certain characteristic, then x /n is called the sample __________.

proportion

5. The probability distribution of x is called a __________ distribution.

sampling

6. The probability distribution of p is called a __________ distribution.

sampling

13. A normal distribution with mean 0 and standard deviation 1 is called the __________ normal distribution.

standard

9. The process of converting a value x from a normal distribution to a z-score is known as __________.

standardization

10. If X is a continuous random variable, then P (X = a) = __________ for any number a.

0

8. As the sample size increases, the sampling distribution of becomes more and more skewed.

False

8. If the points in a normal quantile plot deviate from a straight line, then the population can be treated as approximately normal.

False

15. The probability that a randomly selected value of a continuous random variable lies between a and b is given by the area under the probability density curve between a and b.

True

16. A normal curve is symmetric around its mode.

True

7. If technology is to be used, exact binomial probabilities can be calculated and the normal approximation is not necessary.

True

7. The distribution of p is approximately normal if np ≥ 10 and n (1 −p) ≥ 10.

True