Ok so i hope this app works

The comprehensive strength of concrete is normally distributed with μ = 2500 psi and σ = 50 psi. Find the probability that a ran

VARVARA [1.3K]

Answer:

The probability that the diameter falls in the interval from 2499 psi to 2510 psi is 0.00798.

Step-by-step explanation:

Let's define the random variable, $X =$ "Comprehensive strength of concrete". We have information that $X$ is normally distributed with a mean of 2500 psi and a standard deviation of 50 psi (or a variance of 2500 psi). In other words, $X \sim N(2500, 2500)$ .

We want to know the probability of the mean of X or $\bar{X}$ that falls in the interval $[2499;2510]$ . From inference theory we know that :

$\bar{X} \sim N(2500, \frac{2500}{5}) \Rightarrow \bar{X} \sim N(2500,500)$

Now we can find the probability as follows:

$P(2499 \leq \bar{X} \leq 2510) \Rightarrow P(\frac{2499 - 2500}{500} \leq \frac{\bar{X} - 2500}{500} \leq \frac{2499 - 2500}{500} ) \Rightarrow\\\Rightarrow P(-0.002 \leq \frac{\bar{X} - 2500}{500} \leq 0.02 ) \Rightarrow P(-0.002 \leq Z \leq 0.02 )$

Where $Z \sim N(0,1)$ , then:

$P(-0.002 \leq Z \leq 0.02 ) \approx P(0 \leq Z \leq 0.02 ) = P(Z \leq 0.02 ) - P(Z \leq 0) \\P(0 \leq Z \leq 0.02 ) = 0.50798 - 0.5 = 0.00798$

8 0

3 years ago

lynn takes her puppy, olive, to a doggie daycare. The price for the daycare is 21 per day along with a monthly admission fee of

sashaice [31]

D=426-48(21)
I got 18 days.
So, D=18
Hope this helps! :)

3 0

2 years ago

Read 2 more answers

What is the vertex of the graph of the function below? y = x2 - 8x + 12 A. (-2, 0) B. (-4, -4) C. (-4, 0) D. (-2, -4)

mario62 [17]

To find the vertex of the parabola, we need to write it in a vertex form.

y=x² - 8x +12

1) complete the square

y=x² - 8x +12
y = x² -2*4x + 4² - 4² +12
y=(x-4)² -16 +12

2) calculate and write a vertex
y=(x-4)² -16 +12
y=(x-4)² - 4

(x-4) ----- x- coordinate of the vertex x=4
y=(x-4)² - 4 -------y- coordinate of the vertex y = - 4

Vertex is (4, -4).
Answer is (4, -4). No correct answer is given in choices.