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12 days ago

A hair salon in Cambridge, Massachusetts, reports that on seven randomly selected weekdays, the number of customers who visited

the salon were 40, 30, 28, 22, 36, 16, and 50. It can be assumed that weekday customer visits follow a normal distribution. [You may find it useful to reference the t table.] a. Construct the 90% confidence interval for the average number of customers who visit the salon on weekdays. (Round intermediate calculations to at least 4 decimal places, "sample mean" and "sample standard deviation" to 2 decimal places. Round "t" value to 3 decimal places and final answers to 2 decimal places.)

Mathematics

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Describe in words the surface whose equation is given. (assume that r is not negative.) θ = π/4

tester [12383]

An equation of the form $\theta=\dfrac{\pi}{4}$ describes a line
that passes through the origin and whose tangent corresponds to $\dfrac{\pi}{4}$ . Generally, any equation formatted as $\theta=\theta_0$
represents a line.

7 0

1 month ago

An urn contains 3 red and 7 black balls. Players and withdraw balls from the urn consecutively until a red ball is selected. Fin

Leona [12618]

Correct question:

An urn holds 3 red and 7 black balls. Players A and B take turns withdrawing balls until a red one is chosen. Calculate the probability that A picks the red ball. (A goes first, followed by B, with no replacement of drawn balls).

Answer:

The likelihood that A picks the red ball is 58.33 %

Step-by-step explanation:

A will select the red ball if it is drawn 1st, 3rd, 5th, or 7th.

1st draw: 9C2

3rd draw: 7C2

5th draw: 5C2

7th draw: 3C2

Calculating for all possible scenarios gives us:

9C2 = (9!) / (7!2!) = 36

7C2 = (7!) / (5!2!) = 21

5C2 = (5!) / (3!2!) = 10

3C2 = (3!) / (2!) = 3

Adding these possibilities results in 36 + 21 + 10 + 3 = 70.

The total outcomes for selecting a red ball = 10C3

10C3 = (10!) / (7!3!)

= 120.

The probability that A selects the red ball is determined by dividing the sum of possible events by the overall outcomes.

P( A selects the red ball) = 70 / 120

= 0.5833

= 58.33 %

7 0

2 months ago

If there are 2.2 pounds in 1 kilogram how many pounds are there in x kilograms?

tester [12383]

Answer:

P=x/2.2

Step-by-step explanation:

We can set up an equation to solve this.

Let P represent the number of pounds

Let X represent the number of kilograms

Knowing that 1 kilogram equals 2.2 pounds.

So, if there is 1 kilogram (X) it translates to 2.2 pounds (P).

X=2.2P

Simply rearrange the equation to determine the pounds in x kilograms. Thus, divide both sides by 2.2.

Therefore, we derive P=x/2.2

5 0

1 month ago

WNAE, an all-news AM station, finds that the distribution of the lengths of time listeners are tuned to the station follows the

Inessa [12570]

Answer:

a) $P(X>20)=P(\frac{X-\mu}{\sigma}>\frac{20-\mu}{\sigma})=P(Z>\frac{20-15}{3.5})=P(z>1.43)$

The probability can be determined using the complement rule, with the standard normal distribution, an excel sheet, or a calculator.

$P(z>1.43)=1-P(z$

b) $P(X$

This probability can also be calculated using the normal standard distribution, an excel sheet, or a calculator.

$P(z$

c) $P($

For this one, the probability can likewise be derived from the standard normal distribution, excel, or a calculator, with specific adjustments:

$P(-1.43$

Step-by-step explanation:

Previous concepts

Normal distribution refers to a symmetric probability distribution centered around the mean, indicating that occurrences near the mean are more common than those far from it.

The Z-score is a statistic that represents a value's relationship to the average of a set of values, expressed in terms of how many standard deviations it is away from the mean.

Part a

Let X denote the random variable representing the lengths within a population, and for our case, the distribution for X is as follows:

$X \sim N(15,3.5)$

Where $\mu=15$ and $\sigma=3.5$

We seek the probability:

$P(X>20)$

The most effective way to solve this is by leveraging the normal distribution and the corresponding Z-score:

$z=\frac{x-\mu}{\sigma}$

By applying this formula, we can find the probability:

$P(X>20)=P(\frac{X-\mu}{\sigma}>\frac{20-\mu}{\sigma})=P(Z>\frac{20-15}{3.5})=P(z>1.43)$

Again, this probability can be obtained either using the complement rule, the standard normal distribution, or a calculator.

$P(z>1.43)=1-P(z$

Part b

$P(X$

This probability can also be computed using either the normal standard distribution, an excel sheet, or a calculator.

$P(z$

Part c

$P($

In this case, the probability can similarly be acquired with the help of the standard normal distribution, an excel sheet, or a calculator, with particular adjustments:

$P(-1.43$

5 0

2 months ago

Nina can stitch 2/3 of a dress in 4 hours. If d represents the number of dresses and h represents the number of hours, which equ

tester [12383]

Response:

D=4 hours

Detailed explanation:

5 0

2 months ago