Introduction to expectation

SAT scores (out of 2400) are distributed normally with a mean of 1500 and a standard deviation of 300. Suppose a school council

alekssr [168]

Answer:

10.78% probability this student's score will be at least 2200

Step-by-step explanation:

Normal distribution:

When the distribution is normal, we use 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.

Conditional probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

$\mu = 1500, \sigma = 300$

We pick a recognized student. What is the probability this student's score will be at least 2200

Event A: Recognized(scored at least 1900).

Event B: At least 1900.

Probability of scoring at least 1900.

1 subtracted by the pvalue of Z when X = 1900. So

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

$Z = \frac{1900 - 1500}{300}$

$Z = 1.33$

$Z = 1.33$ has a pvalue of 0.9082.

1 - 0.9082 = 0.0918.

So P(A) = 0.0918

Intersection:

The intersection between at least 1900 and at least 2200 is at least 2200.

Probability:

1 subtracted by the pvalue of Z when X = 2200. So

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

$Z = \frac{2200 - 1500}{300}$

$Z = 2.33$

$Z = 2.33$ has a pvalue of 0.9901.

So $P(A \cap B) = 1 - 0.9901 = 0.0099$

Then

$P(B|A) = \frac{0.0099}{0.0918} = 0.1078$

10.78% probability this student's score will be at least 2200

4 0

3 years ago

Given that the acceleration vector is a(t)=(-4cos(2t),-4sin(2t),t)

fiasKO [112]

Answer:

a(t) = (-2sin2, -2cos0, (1/2)

r(t) = (cos2, sin2, 1/6)

Step-by-step explanation:

By definition, given a position vector, r(t),

- The velocity vector v(t) is the derivative of the position vector.

v(t) = r'(t)

- The acceleration vector a(t) is the derivative of the velocity vector.

a(t) = v'(t) = r''(t).

Knowing that integration is the reverse of differentiation, we can obtain the velocity and position vectors from the given acceleration vector.

a(t) = (-4cos(2t), -4sin(2t), t)

Integrating with respect t, we have:

v(t) = (-4/2)sin(2t), (-4/2)(-cos(2t)), (1/2)t²)

at (1, 0, 1), a(t) = (-2sin2, -2cos0, (1/2)(1))

= (-0.0698, -2, 0.5)

Now, we integrate the velocity vector with respect to t to obtain the position vector.

r(t) = (cos(2t), sin(2t), (1/6)t³)

at (1, 1, 1)

r(t) = (cos2, sin2, 1/6)

= (0.999, 0.035, 0.167)

3 0

3 years ago

Find the measure of angle A<br>(look at pic pls help)<br><br><br>A- 120<br>B- 300<br>C- 60<br>D- 90

aleksklad [387]

Answer: 300

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

6) A jet travels 480 miles in 2 hours. At this rate, how far could the jet fly in

Sveta_85 [38]

I need help on this too

7 0

3 years ago

Read 2 more answers

. A circulating pump consumes 450 W for 24 hr a day. a. Determine the energy consumed for a one-year period. b. Calculate the ut

Anit [1.1K]

Answer:

a. 3942 kWh

b. $473.04

c. 1314 kWh

d. $157.68

Step-by-step explanation:

There are 1000 W in 1 kW, so 450 W = 0.450 kW. The energy used per day is ...

(0.45 kW)(24 h) = 10.8 kWh . . . . energy per day

Then in a 365-day year, the energy used is

(365 da/yr)(10.8 kWh/da) = 3942 kWh/yr

__

At the rate of $0.12/kWh, the cost of running the pump is ...

($0.12/kWh)(3942 kWh/yr) = $473.04/yr

__

Switching the pump off for 1/3 of the time will save 1/3 of the energy found in part (a):

1/3(3942 kWh) = 1314 kWh . . . . energy saved by switching off the pump

__

The savings will be 1/3 of the cost of running the pump full time:

1/3($473.04/yr) = $157.68/yr

4 0

2 years ago