Which point on the number line best represents √67?

A student was marked tardy five different times in a 40 day period. What percent of the time was the student tardy?

Reptile [31]

Answer:

12.5%

Step-by-step explanation:

5/40 = .125

.125×100 = 12.5%

4 0

3 years ago

Comparing observations from different populations: The heights of adult men in America are normally distributed, with a mean of

Schach [20]

Answer:

a. Z = 1.99

b. 97.67%

c. Z = 2.56

d. 0.52%

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

a. If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)?

The heights of adult men in America are normally distributed, with a mean of 69.7 inches and a standard deviation of 2.66 inches, and thus, we have $\mu = 69.7, \sigma = 2.66$

6 feet 3 inches = 6*12 + 3 = 75 inches, which means that we have to find z when X = 75. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{75 - 69.7}{2.66}$

$Z = 1.99$

b. What percentage of men are SHORTER than 6 feet 3 inches?

The proportion is the p-value of Z = 1.99.

Looking at the z-table, Z = 1.99 has a p-value of 0.9767.

0.9767*100% = 97.67%, which is the answer.

c. If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)?

The heights of adult women in America are also normally distributed, but with a mean of 64.5 inches and a standard deviation of 2.54 inches, and thus, we have $\mu = 64.5, \sigma = 2.54$ . We have to find Z when X = 5*12 + 11 = 71. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{71 - 64.5}{2.54}$

$Z = 2.56$

d. What percentage of women are TALLER than 5 feet 11 inches?

The proportion is 1 subtracted by the p-value of Z = 2.56.

Looking at the z-table, Z = 2.56 has a p-value of 0.9948.

1 - 0.9948 = 0.0052

0.0052*100% = 0.52%, which is the answer.

3 0

3 years ago

Three shoppers from the survey are selected at random, one at a time without replacement. What is the probability that none of t

Travka [436]

Answer:

0.395

Step-by-step explanation:

The computation of the probability that none of the three shoppers purchased electronics is shown below:

So, first we have to determine the number of shoppers without considering the purchase i.e

= Total number of shoppers - electronics

where,

Total number of shoppers = Offices supplies + electronics + clothing + beauty supplies - electronics

= 18 + 25 + 40 + 12 - 25

= 95 - 25

= 70

Now the probability is

= $\frac{70}{95}\times\frac{69}{94}\times\frac{68}{93}$

= 0.395

5 0

3 years ago

There are 50 students in a calculus class. The amount of time needed for the instructor to grade a randomly chosen midterm exam

natta225 [31]

Answer:

14.46% probability that the instructor can finish grading in 4 and a half hours

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For sums of n values from a distribution, the mean is $n\mu$ and the standard deviation is $s = \sqrt{n}\sigma$

In this problem, we have that:

$\mu = 6*50 = 300, s = \sqrt{50}*4 = 28.2843$

What is the probability that the instructor can finish grading in 4 and a half hours

Four and half hours is 4.5*60 = 270.

So this probability is the pvalue of Z when X = 270.

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{270 - 300}{28.2843}$

$Z = -1.06$

$Z = -1.06$ has a pvalue of 0.1446

14.46% probability that the instructor can finish grading in 4 and a half hours

8 0

3 years ago

If the circular opening of the pipe has a diameter of 21 inches and the oil was estimated to be flowing at 30 inches/second, how

Anestetic [448]

This is a matter of Amount = Rate times time.

First, find the area of the circular opening. A = pi (r^2). Here,

A = pi(10.5 inches)^2.

To obtain the volume of water that flows out of the pipe per second, multiply this area by the 30 inches per second rate.

That comes out to a volume per second of Volume rate = pi*(10.5 inches)^2 * 30 inches per second:

Volume rate = 3.14(110.25 in^2)(30 inches/sec)
= 10390.8 cubic inches per second

Convert this result to cubic feet per second. Recall that 1 cubic foot = (12 inches)^3, or 1728 cubic inches / 1 cubic foot.

Thus, 10390.8 cubic inches per second comes out to

10390.8 cubic inches
---------------------------- = Just over 6 cubic feet per sec.
1728 cu. inches
---------------------
1 cu. ft

How many sec in 1 day? 1 day = 24 hours
1 hour = 60 minutes
60 seconds = 1 minute

Figure out how many seconds there are in 1 day, and then multiply your result by 6 cu. ft. / sec.

8 0

3 years ago