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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

Carina begins to solve the equation -4 - 2/3x = -6 by adding 4 to both sides. Which statements regarding the rest of the solving

Andru [333]

Answer:

A.) After adding 4 to both sides, the equation is $-\frac{2}{3}x=-2$

C.) The equation can be solved for x using exactly one more step by multiplying both sides by $-\frac{3}{2}$

D.) The equation can be solved for x using exactly one more step by dividing both sides by $-\frac{2}{3}$

Step-by-step explanation:

The correct questions is as follows:

Carina begins to solve the equation -4-2/3x=-6 by adding 4 to both sides. Which statements regarding the rest of the solving process could be true? Check all that apply.

A.) After adding 4 to both sides, the equation is -2/3x=-2.

B.) After adding 4 to both sides, the equation is -2/3x=-10 .

C.) The equation can be solved for x using exactly one more step by multiplying both sides by -3/2.

D.) The equation can be solved for x using exactly one more step by dividing both sides by -2/3.

E.) The equation can be solved for x using exactly one more step by multiplying both sides by -2/3.

Given equation:

$-4-\frac{2}{3}x=-6$

To show the steps we will carry out in order to solve for $x$

Solution:

Solving for $x$

Step 1:

Adding both sides by 4

$4-4-\frac{2}{3}x=-6+4$

Thus, we get:

$-\frac{2}{3}x=-2$

Thus statement A is correct.

Step 2:

Multiplying both sides by $-\frac{3}{2}$

$-\frac{3}{2}\times -\frac{2}{3}x=-2\times -\frac{3}{2}$

Thus, we get:

$x=3$ [Two negatives multiply to give a positive]

This proves that statement C is correct.

Or Step 2:

Dividing both sides by $-\frac{2}{3}$

$\frac{-\frac{2}{3}x}{-\frac{2}{3}}=\frac{-2}{-\frac{2}{3}}$

Thus, we get:

$x=-2\times -\frac{3}{2}$ [On dividing with a fractional divisor, we take reciprocal and multiply it with the dividend.]

$x=3$ [Two negatives multiply to give a positive]

This prove that statement D is correct.

5 0

2 years ago

Let P be a point between points S and T on 2004-01-01-02-00_files/i0120000.jpg. If ST = 21, SP = 3b – 11, and PT = b + 4, solve

NNADVOKAT [17]

The best and most correct answer among the choices provided by your question is the third choice or letter C.

<span>If ST = 21, SP = 3b – 11, and PT = b + 4, the value of b would be 14.

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I hope my answer has come to your help. God bless and have a nice day ahead!

7 0

2 years ago

Read 2 more answers

Jacob is twice as heavy as Ken Linda is half as heavy as Ken Giver 3 children is at least 35 kg. a By letting Linda's mass be x,

Usimov [2.4K]

==> she can buy 45 notebooks at most.

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