A) 93<br>B) 85<br>C) 107<br>D) 79

slavikrds [6]

3/9 is the answer I got

5 0

4 years ago

The amount of time that people spend at Grover Hot Springs Spa is normally distributed with a mean of 63 minutes and a standard

PtichkaEL [24]

Answer:

a) $X \sim N(63,18)$

Where $\mu=63$ and $\sigma=18$

b) $P(X>90)=P(\frac{X-\mu}{\sigma}>\frac{90-\mu}{\sigma})=P(Z>\frac{90-63}{18})=P(Z>1.5)$

And we can find this probability using the complement rule and with the normal standard table or excel:

$P(Z>1.5)=1-P(Z$

c) $P(X$

$P(Z$

d) $P(60$

$P(-0.167$

e) IQR = 75.13-50.87=24.26

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the amount of time that people spend at Grover Hot Springs of a population, and for this case we know the distribution for X is given by:

$X \sim N(63,18)$

Where $\mu=63$ and $\sigma=18$

Part b

We are interested on this probability

$P(X>90)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

If we apply this formula to our probability we got this:

$P(X>90)=P(\frac{X-\mu}{\sigma}>\frac{90-\mu}{\sigma})=P(Z>\frac{90-63}{18})=P(Z>1.5)$

And we can find this probability using the complement rule and with the normal standard table or excel:

$P(Z>1.5)=1-P(Z$

Part c

We are interested on this probability

$P(X$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

If we apply this formula to our probability we got this:

$P(X$

And we can find this probability using the normal standard table or excel:

$P(Z$

Part d

If we apply this formula to our probability we got this:

$P(60$

And we can find this probability with this difference:

$P(-0.167$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(-0.167$

Part e

Q1

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.75$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.25 of the area on the left and 0.75 of the area on the right it's z=-0.674. On this case P(Z<-0.674)=0.25 and P(z>-0.674)=0.75

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=-0.674$

And if we solve for a we got

$a=63 -0.674*18=50.87$

So the value of height that separates the bottom 25% of data from the top 75% is 50.87.

Q3

Since the distribution is symmetrical we repaeat the procedure for Q1 but now with z= 0.674

$z=0.674$

And if we solve for a we got

$a=63 +0.674*18=75.13$

And then the IQR = 75.13-50.87=24.26

3 0

3 years ago

C. if matrix a is diagonalizable, find the diagonal matrix d that is associated with a by using d

dalvyx [7]

Answering this question is not within my ability. i apologize for my incompetence and hope you can find it in your heart to forgive me. lmou

7 0

3 years ago

3 over 2 of 24 bananas=

Neko [114]

Answer: 36 bananas

Step-by-step explanation: find 1/2 of 24 which is 12. Then, add that with 24.

4 0

3 years ago

Consider the following pair of equations: y = −2x 8 y = x − 1 Explain how you will solve the pair of equations by substitution.

NARA [144]

If so y= -2x and 8y=x-1...

solution:

$y=-2x \\ \\ 8y=x-1 \Rightarrow \\ \\ 8.(-2x)=x-1 \Rightarrow \\ \\ -16x=x-1 \Rightarrow \\ \\ 17x=1 \Rightarrow \\ \\ x=\dfrac{1}{17}$

8 0

3 years ago

Read 2 more answers

A) 93B) 85C) 107D) 79