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garik1379 [7]
3 years ago
13

The distribution of math SAT scores is normally distributed with a mean of 500 and a standard deviation of 90.

Mathematics
1 answer:
IrinaVladis [17]3 years ago
8 0

Answer:

a) 1.39%

b) 42.26%

c) 97.72%

d) 7.78%

e) 99.01%

Step-by-step explanation:

mean (μ) = 500, standard deviation (σ) = 90

The z score is used to measure the amount by which the raw score is above or below the mean. It is given by:

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

a) For x > 700

z=\frac{x-\mu}{\sigma}=\frac{700-500}{90} =2.22

From the probability distribution table:

P(x > 700) = P(z > 2.22) = 1 - P(z < 2.22) = 1 -0.9861 = 0.0139 = 1.39%

b) For x = 450

z=\frac{x-\mu}{\sigma}=\frac{450-500}{90} =-0.56

For x = 550

z=\frac{x-\mu}{\sigma}=\frac{550-500}{90} =0.56

From the probability distribution table:

P(450< x < 550) = P(z < 0.56) - P(z < -0.56) = 0.7123 - 0.2877 = 0.4246 = 42.46%

c) For x < 680

z=\frac{x-\mu}{\sigma}=\frac{680-500}{90} =2

From the probability distribution table:

P(x < 680) = P(z < 2) = 0.9772 = 97.72%

d) From the probability distribution table: P(z < -1.42) = 0.0778 = 7.78%

e) c) For x = 710

z=\frac{x-\mu}{\sigma}=\frac{710-500}{90} =2.33

From the probability distribution table: P(x < 710) = P(z < 2.33) = 0.9901 = 99.01%

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Answer:

DOC = 70

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Step-by-step explanation:

AOB is supplementary to BOC and AOD, which means together they equal 180. 180-70=110, so BOC and AOD are both 110.

AOB and DOC are vertical angles to each other, so are AOD and BOC. Vertical angles are always equal to each other. So since AOB is 70, so is DOC.

Hope this makes sense:)

5 0
3 years ago
In right triangle DEF, ∠E is a right angle, m∠D=26∘, and DF=4.5.
jok3333 [9.3K]

Answer:

The measurement of EF is 1.98 units

Step-by-step explanation:

In Δ DEF

∵ m∠E = 90°

∴ FD is the hypotenuse of the triangle

∵ m∠D = 26°

∵ EF is opposite to angle D

- We can use the sine ratio to find it

∵ sin D = \frac{EF}{FD} ⇒ (opposite side / hypotenuse)

∵ FD = 4.5 units

∴ sin(26) = \frac{EF}{4.5}

- Multiply both sides by 4.5

∴ 4.5 sin(26) = EF

∵ sin 26° ≈ 0.44

∴ 4.5(0.44) = EF

∴ 1.98 = EF

The measurement of EF is 1.98 units

3 0
3 years ago
Simplify completely.<br><br> (w15/w5)4<br><br> Enter your answer in the box.
Vlad [161]

Answer:w40

Step-by-step explanation:

w15/w5 = w10

(w10)^4 = w40

3 0
3 years ago
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
ch4aika [34]

Answer: -258

<u>Step-by-step explanation:</u>

Given the sequence {-8, 16, -32, 64, ... , a₇} we know the following

  • the first term (a₁) = -8
  • the common ratio (r) = -2
  • the number of terms (n) = 7

Input the information above into the Sum formula:

S_n=\dfrac{a_1(1-r^n)}{1-r}\\\\S_7=\dfrac{-8(1-(-2)^7)}{1-(-2)}\\\\.\quad =\dfrac{-8(1-(-128))}{1+3}\\\\.\quad =\dfrac{-8(129)}{4}\\\\.\quad =-2(129)\\\\.\quad =-258

3 0
3 years ago
Read 2 more answers
The probability that a student chosen at random from your class is a psychology major is .18. What is the probability that a stu
devlian [24]

Answer:  0.82

Step-by-step explanation:

We know that :

For any event A , the probability of not getting A is given by :-

P(not A)= 1- P(A)

Given : The probability that a student chosen at random from your class is a psychology major is P( psychology major) =0.18.

Then, the probability that a student chosen at random from your class is not a psychology major will be :

P(not psychology major)= 1 - P(psychology major)

= 1-0.18=0.82

Hence, the probability that a student chosen at random from your class is not a psychology major= 0.82

5 0
3 years ago
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