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gtnhenbr [62]
3 years ago
12

The final scores of students in a graduate course are distributed normally with a mean of 72 and a standard deviation of 5. What

is the probability that a student's score will be between 65 and 78?
Mathematics
1 answer:
Tcecarenko [31]3 years ago
8 0

Answer:

0.8041

Step-by-step explanation:

We know that  

μ=72  and  σ=5

and P(65<X<78)

We can determine the Z value as (X-μ)/σ

P( 65<X<78 )=P( 65-72< X-μ<78-72)

P((65-72)/5

P(65

To fine the Z values:

P (-1.4

From the standard normal tables:

P (Z

to find P ( Z<-1.4)

P ( Z

From the standard normal tables:

P ( Z

Therefore

P(-1.4

P (65

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10 &lt; 0.25 ( x + 1 ) &lt; 11
AURORKA [14]
10 <0.25 (x + 1) <11
 
We must solve two inequalities in this case.
 Inequality 1:
 
10 <0.25 (x + 1)
 10 / 0.25 <x + 1
 40 <x + 1
 40-1 <x
 39 <x
 Inequality 2:
 
0.25 (x + 1) <11
 (x + 1) <11 / 0.25
 (x + 1) <44
 x <44-1
 x <43
 The final result is:
 39 <x <43
 Answer:
 
39 <x <43
6 0
3 years ago
Let f(x) = 3x + 5 and g(x) = x2.
Nadusha1986 [10]

Answer:

f(x^2)=3x^2+5

Step-by-step explanation:

math

4 0
3 years ago
According to the National Vital Statistics, full-term babies' birth weights are Normally distributed with a mean of 7.5 pounds a
Sav [38]

Answer:

68.26% probability that a randomly selected full-term pregnancy baby's birth weight is between 6.4 and 8.6 pounds

Step-by-step explanation:

Problems of normally distributed samples are solved using 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.

In this problem, we have that:

\mu = 7.5, \sigma = 1.1

What is the probability that a randomly selected full-term pregnancy baby's birth weight is between 6.4 and 8.6 pounds

This is the pvalue of Z when X = 8.6 subtracted by the pvalue of Z when X = 6.4. So

X = 8.6

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

Z = \frac{8.6 - 7.5}{1.1}

Z = 1

Z = 1 has a pvalue of 0.8413

X = 6.4

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

Z = \frac{6.4 - 7.5}{1.1}

Z = -1

Z = -1 has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

68.26% probability that a randomly selected full-term pregnancy baby's birth weight is between 6.4 and 8.6 pounds

6 0
3 years ago
Will give brainliest to the first or those who ask
xxMikexx [17]

Its the one at the very bottom. :)

8 0
2 years ago
Read 2 more answers
Given: ∆AMK, MP ⊥ AK , MP = 10 m∠A = 72º, m∠PMK = 50° Find AM, MK, AK
mina [271]

Answer:

Step-by-step explanation:

The diagram of triangle AMK is shown on the attached photo. To determine AM, we would apply trigonometric ratio since triangle AMP is a right angle triangle.

Sin# = opposite/hypotenuse

Sin 72 = 10/AM

AMSin72 = 10

AM = 10/Sin72 = 10/0.9511

AM = 10.51

To determine MK,

Cos# = adjacent/hypotenuse

Cos 50 = 10/MK

MKCos50 = 10

MK = 10/Cos50 = 10/0.6428

MK = 15.6

AK = AP + KP

Tan# = opposite/adjacent

Tan 72 = 10/AP

AP tan 72 = 10

AP =10/tan72 = 10/ 3.0777 = 3.25

Tan 50 = KP/10

KP = 10tan50

KP= 10× 1.1918 = 11.918

Therefore,

AK = 3.25 + 11.918 = 15.168

3 0
2 years ago
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