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12 days ago

7

What teacher exhibited the most consistent performance over this 5 year span

1 answer:

lawyer [4K]12 days ago

4 0

Is there meant to be an image?

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Use the normal approximation to the binomial distribution to answer this question. Fifteen percent of all students at a large un

AnnZ [3877]

Answer: 0.1289

Step-by-step explanation:

Given: The proportion of students absent on Mondays at a large university.: $p=0.15$

Sample size: $n=12$

Mean: $\mu=np=12\times0.15=1.8$

Standard deviation = $\sigma=\sqrt{np(1-p)}$

$\Rightarrow\ \sigma=\sqrt{12(0.15)(1-0.15)}=1.23693168769\approx1.2369$

Let x represent a binomial variable.

Referencing the standard normal distribution table,

$P(x=4)=P(x\leq4)-P(x\leq3)$ (1)

Z score for normal distribution:-

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

For x=4

$z=\dfrac{4-1.8}{1.2369}\approx1.78$

For x=3

$z=\dfrac{3-1.8}{1.2369}\approx0.97$

Thus, from (1)

$P(x=4)=P(z\leq1.78)-P(z\leq0.97)\\\\=0.962462-0.8339768\approx0.1289$

Consequently, the likelihood of four students being absent = $0.1289$

3 0

16 hours ago

1199.28856995 to the nearest ten

lawyer [4008]

Hey! Hi! Hola! Aloha!

When rounding 1199.28856995 to the nearest tenth, the result is 119.3.

I hope this is helpful!

4 0

9 days ago

Read 2 more answers

Ms. Gallegos burns 236 calories riding her bike each hour. She wants to burn more than 590 calories riding her bike at the same

Svet_ta [4321]

Response:

354

Detailed explanation:

5 0

4 days ago

As a part-time contractor, you want to test a new cement mixture for a project. You need 2 34 wheelbarrows of sand to make 8 whe

zzz [4022]

Answer: He will require 10.07 cubic feet of sand for the wheelbarrows.

Step-by-step explanation:

Given that

the ratio of wheelbarrows filled with sand to those filled with concrete is expressed as

$2\dfrac{3}{4}:8\\\\=\dfrac{11}{4}:8\\\\=11:32$

The volume of concrete in wheelbarrows is 248 cubic feet.

Then the volume of sand in wheelbarrows can be found as

$(\dfrac{11}{32})^3=\dfrac{x}{248}\\\\\dfrac{1331\times 248}{32^3}=x\\\\10.07=x$

Therefore, he will require 10.07 cubic feet of sand for the wheelbarrows.

7 0

7 days ago

Read 2 more answers

Water is poured into a conical paper cup at the rate of 3/2 in3/sec (similar to Example 4 in Section 3.7). If the cup is 6 inche

tester [3916]

Response:

The height of the water when it reaches 4 inches is $\frac{3}{8\times \pi} inch/s$ .

Detailed Explanation:

Flow rate of water from the cone = R= $\frac{3}{2} inch^3/s$

Height of the cup = h = 6 inches

Radius of the cup = r = 3 inches

$\frac{r}{h}=\frac{3 inch}{6 inch}=\frac{1}{2}$

r = h/2

Volume of the cone = $V=\frac{1}{3}\pi r^2h$

$V=\frac{1}{3}\pi r^2h$

$\frac{dV}{dt}=\frac{d(\frac{1}{3}\pi r^2h)}{dt}$

$\frac{dV}{dt}=\frac{d(\frac{1}{3}\pi (\frac{h}{2})^2h)}{dt}$

$\frac{dV}{dt}=\frac{1}{3\times 4}\pi \times \frac{d(h^3)}{dt}$

$\frac{dV}{dt}=\frac{1\pi }{12}\times 3h^2\times \frac{dh}{dt}$

$\frac{3}{2} inch^3/s=\frac{1\pi }{12}\times 3h^2\times \frac{dh}{dt}$

h = 4 inches

$\frac{3}{2} inch^3/s=\frac{1\pi }{12}\times 3\times (4inches )^2\times \frac{dh}{dt}$

$\frac{3}{2} inch^3/s=\pi\times 4\times \frac{dh}{dt} inches^2$

$\frac{dh}{dt}=\frac{3}{8\times \pi} inch/s$

The height of the water when it is 4 inches deep is $\frac{3}{8\times \pi} inch/s$ .

6 0

11 days ago