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Vlad [161]
3 years ago
5

86[]×[]=2325

Mathematics
1 answer:
forsale [732]3 years ago
8 0

Answer:

235

Step-by-step explanation:

The square root of 55,225 is = 235

because,

235 x 235 = 55,225

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In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal dist
Marrrta [24]

Answer:

a) Bi [P ( X >=15 ) ] ≈ 0.9944

b) Bi [P ( X >=30 ) ] ≈ 0.3182

c)  Bi [P ( 25=< X =< 35 ) ] ≈ 0.6623

d) Bi [P ( X >40 ) ] ≈ 0.0046  

Step-by-step explanation:

Given:

- Total sample size n = 745

- The probability of success p = 0.037

- The probability of failure q = 0.963

Find:

a. 15 or more will live beyond their 90th birthday

b. 30 or more will live beyond their 90th birthday

c. between 25 and 35 will live beyond their 90th birthday

d. more than 40 will live beyond their 90th birthday

Solution:

- The condition for normal approximation to binomial distribution:                                                

                    n*p = 745*0.037 = 27.565 > 5

                    n*q = 745*0.963 = 717.435 > 5

                    Normal Approximation is valid.

a) P ( X >= 15 ) ?

 - Apply continuity correction for normal approximation:

                Bi [P ( X >=15 ) ] = N [ P ( X >= 14.5 ) ]

 - Then the parameters u mean and σ standard deviation for normal distribution are:

                u = n*p = 27.565

                σ = sqrt ( n*p*q ) = sqrt ( 745*0.037*0.963 ) = 5.1522

- The random variable has approximated normal distribution as follows:

                X~N ( 27.565 , 5.1522^2 )

- Now compute the Z - value for the corrected limit:

                N [ P ( X >= 14.5 ) ] = P ( Z >= (14.5 - 27.565) / 5.1522 )

                N [ P ( X >= 14.5 ) ] = P ( Z >= -2.5358 )

- Now use the Z-score table to evaluate the probability:

                P ( Z >= -2.5358 ) = 0.9944

                N [ P ( X >= 14.5 ) ] = P ( Z >= -2.5358 ) = 0.9944

Hence,

                Bi [P ( X >=15 ) ] ≈ 0.9944

b) P ( X >= 30 ) ?

 - Apply continuity correction for normal approximation:

                Bi [P ( X >=30 ) ] = N [ P ( X >= 29.5 ) ]

- Now compute the Z - value for the corrected limit:

                N [ P ( X >= 29.5 ) ] = P ( Z >= (29.5 - 27.565) / 5.1522 )

                N [ P ( X >= 29.5 ) ] = P ( Z >= 0.37556 )

- Now use the Z-score table to evaluate the probability:

                P ( Z >= 0.37556 ) = 0.3182

                N [ P ( X >= 29.5 ) ] = P ( Z >= 0.37556 ) = 0.3182

Hence,

                Bi [P ( X >=30 ) ] ≈ 0.3182  

c) P ( 25=< X =< 35 ) ?

 - Apply continuity correction for normal approximation:

                Bi [P ( 25=< X =< 35 ) ] = N [ P ( 24.5=< X =< 35.5 ) ]

- Now compute the Z - value for the corrected limit:

                N [ P ( 24.5=< X =< 35.5 ) ]= P ( (24.5 - 27.565) / 5.1522 =<Z =< (35.5 - 27.565) / 5.1522 )

                N [ P ( 24.5=< X =< 25.5 ) ] = P ( -0.59489 =<Z =< 1.54011 )

- Now use the Z-score table to evaluate the probability:

                P ( -0.59489 =<Z =< 1.54011 ) = 0.6623

               N [ P ( 24.5=< X =< 35.5 ) ]= P ( -0.59489 =<Z =< 1.54011 ) = 0.6623

Hence,

                Bi [P ( 25=< X =< 35 ) ] ≈ 0.6623

d) P ( X > 40 ) ?

 - Apply continuity correction for normal approximation:

                Bi [P ( X >40 ) ] = N [ P ( X > 41 ) ]

- Now compute the Z - value for the corrected limit:

                N [ P ( X > 41 ) ] = P ( Z > (41 - 27.565) / 5.1522 )

                N [ P ( X > 41 ) ] = P ( Z > 2.60762 )

- Now use the Z-score table to evaluate the probability:

               P ( Z > 2.60762 ) = 0.0046

               N [ P ( X > 41 ) ] =  P ( Z > 2.60762 ) = 0.0046

Hence,

                Bi [P ( X >40 ) ] ≈ 0.0046  

4 0
3 years ago
Pls help meeee I don’t understand this at alll
balu736 [363]

Answer:

you need the formula for the cone , Korc

Step-by-step explanation:

formula for cone = \frac{1}{3}*π*r^{2}*h

they tell us that the diameter is 8 so  r = 4

and that h = 9

volume of cone = \frac{1}{3}*π*4^{2}*9

VoC = 150.796

VoC = 150.8  ( to the nearest 10th)

5 0
3 years ago
A rectangle has a height of 2x^4 with a width of x^2+8x+15. Express the area of the rectangle.
Amiraneli [1.4K]

Hi there!

We know that the formula for the area of a rectangle is height * width. Thus, we can multiply these two expressions together:

2x^4\cdot (x^2+8x+15)\\

Now, we know through the distributive property that we can distribute the 2x^4\\ to everything in the parenthesis. Once this is done, we get:

2x^4 \cdot x^2+2x^4\cdot8x+2x^4\cdot15

Now, we know through the power rule that when two exponents are multiplied together with the same base, the exponent can be added together (x^a \cdot x^b = x^{a+b}). This then would make our equation:

2x^{4+2}+16x^{4+1}+30x^4\\

Giving us for our final answer:

2x^{6}+16x^{5}+30x^4\\

Hope this helps!

8 0
2 years ago
If Y is directly proportional to the square root of X and Y equals -32 when X equals 400, find Y if X equals 160,000
yan [13]

Answer:

Step-by-step explanation:

4 0
2 years ago
(-4, 12) and (-7, -3)​
Alinara [238K]

Answer:

The slope is 5/1 or 5

Step-by-step explanation:

Hope this helps!

8 0
2 years ago
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