BUAL 2

In a manufacturing process, a random sample of 9 manufactured bolts has a mean length of 3 inches with a variance of .09 and is normally distributed. What is the 90 percent confidence interval for the true mean length of the manufactured bolt?

2.8140 to 3.1860 [x¯ ± tα/2, n−1(s/n−−√)]= [3±1.86(.3/3)]=[3±.186]=[2.814, 3.186]

In a manufacturing process, a random sample of 36 manufactured bolts has a mean length of 3 inches with a standard deviation of .3 inches. What is the 99 percent confidence interval for the true mean length of the manufactured bolt?

2.864 to 3.136 [x±tα/2,n−1(s/n−−√)]=[3±2.719(.3/6)]=[3±.136]=[2.864, 3.136]

In a manufacturing process, we are interested in measuring the average length of a certain type of bolt. Past data indicate that the standard deviation is .25 inches. How many manufactured bolts should be sampled in order to make us 95 percent confident that the sample mean bolt length is within .02 inches of the true mean bolt length?

601 n = [(zα/2 × s)/E]2 = [(1.96 × .25)/.02]2 = 600.25 = 601

Which of the following statements is not a property of the normal probability distribution?

95.44 percent of all possible observed values of the random variable x are within plus or minus three standard deviations of the population mean.

If the random variable x is normally distributed, ______ percent of all possible observed values of x will be within three standard deviations of the mean.

99.73

Rejecting a true null hypothesis is called a ________ error.

Type I

________ says that if the sample size is sufficiently large, then the sample means are approximately normally distributed.

The Central Limit Theorem

As the standard deviation (σ) decreases, the width of the confidence interval ________

decreases

The area under the curve of a valid continuous probability distribution must ________.

equal 1

For nonnormal populations, as the sample size (n) ________, the distribution of sample means approaches a(n) ________ distribution.

increases, normal

________ values of the standard deviation result in a normal curve that is wider and flatter.

larger

The specific shape of each normal distribution is determined by its ________ and ________.

mean, standard deviation.

The normal approximation of the binomial distribution is appropriate when

np ≥ 5 and n(1 − p) ≥ 5.

The exact spread of the t distribution depends on the _______

number of degrees of freedom

A recent study conducted by the state government attempts to determine whether the voting public supports a further increase in cigarette taxes. The opinion poll recently sampled 1,500 voting age citizens. 1,020 of the sampled citizens were in favor of an increase in cigarette taxes. The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66. Identify the null hypothesis.

p ≤ .66

It is appropriate to use the uniform distribution to describe a continuous random variable x when

relative frequencies of all possible values of x are about the same.

A confidence interval for the population mean is an interval constructed around the ________

sample mean

The z value tells us the number of ________ that a value of x is from the mean.

standard deviations

In testing H0: μ = 23; versus HA: μ > 23 using the critical value rule, when x¯x¯ = 26, s = 6, and n = 20, what is the value of the test statistic? Assume that the population from which the sample is selected is normally distributed.

t=(26-23) / ((6)/(sqrt20)) =2.24

The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams. We calculated the value of z for a specific box of this brand of cereal, and the z value was negative. This negative z value indicates that

the fill weight is less than 910 grams

When the population is normally distributed, population standard deviation σ is unknown, and the sample size is n = 15, the confidence interval for the population mean μ is based on

the t distribution.

A continuous probability distribution having a rectangular shape, where the probability is evenly distributed over an interval of numbers is a(n) ________ distribution.

uniform

Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 ounces and a standard deviation of .2 ounces. The weights of the sugar packages are normally distributed. What is the probability that 16 randomly selected packages will have a weight in excess of 16.075 ounces?

.0668 P[z > (16.075 − 16)/(.2/√16)] = P(z > 1.5) = 1.00 − .9332 = .0668

Find P(x¯x¯ < 35) if μ = 40, σx = 16, n = 16.

.1056

Given that the length an athlete throws a hammer is a normal random variable with mean 50 feet and standard deviation 5 feet, what is the probability he throws it no less than 55 feet?

.1587 Z = (55 − 50)/5 = 1 P(X ≥ 55) = 1 − .8412 = .1587

What is the probability that a standard normal random variable will be between .3 and 3.2?

.3814

Find P(x¯x¯ > 172), if μ = 175 and σ2xσx2 = 9.

.8413

The mean of a standard normal distribution is always equal to ________.

0