Double the product of u and 7

Consider a binomial experiment with n = 10 and p = 0.10. (a) Compute f(0). If required, round your answer to four decimal places

ss7ja [257]

Answer:

(a) The value of f (0) is 0.3487.

(b) The value of f (2) is 0.1937.

(c) The value of P (X ≤ 2) is 0.9298.

(d) The value of P (X ≥ 1) is 0.6513.

(e) The value of E (X) is 1.

(f) The value of V (X) is 0.9 and σ is 0.9487.

Step-by-step explanation:

The random variable X follows a Binomial distribution with parameter n = 10 and p = 0.10.

The probability mass function of X is:

$P(X=x)={10\choose x}0.10^{x}(1-0.10)^{10-x};\ x=0,1,2,3...$

(a)

Compute the value of f (0) as follows:

f (0) = P (X = 0)

$={10\choose 0}0.10^{0}(1-0.10)^{10-0}\\=1\times 1\times 0.348678\\=0.348678\\\approx0.3487$

Thus, the value of f (0) is 0.3487.

(b)

Compute the value of f (2) as follows:

f (2) = P (X = 2)

$={10\choose 2}0.10^{2}(1-0.10)^{10-2}\\=45\times 0.01\times 0.43047\\=0.1937115\\\approx0.1937$

Thus, the value of f (2) is 0.1937.

(c)

Compute the value of P (X ≤ 2) as follows:

P (X ≤ 2) = P (X = 0) + P (X = 1) + P (X = 2)

$=\sum\limits^{0}_{2} {{10\choose x}0.10^{x}(1-0.10)^{10-x}}\\=0.3487+0.3874+0.1937\\=0.9298$

Thus, the value of P (X ≤ 2) is 0.9298.

(d)

Compute the value of P (X ≥ 1) as follows:

P (X ≥ 1) = 1 - P (X < 1)

= 1 - P (X = 0)

= 1 - 0.3487

= 0.6513

Thus, the value of P (X ≥ 1) is 0.6513.

(e)

Compute the expected value of X as follows:

$E(X)=n\times p$

$=10\times 0.10\\=1$

Thus, the value of E (X) is 1.

(f)

Compute the variance of X as follows:

$V(X)=np(1-p)$

$=10\times 0.10\times (1-0.10)\\=0.90$

Compute the standard deviation of X as follows:

$SD(X)=\sqrt{V(X)}$

$=\sqrt{0.90}\\=0.94868\\\approx0.9487$

Thus, the value of V (X) is 0.9 and σ is 0.9487.

8 0

4 years ago

The average length of a king cobra is 118 inches, which is 22 inches longer than a black mamba. Write and solve an equation to f

Agata [3.3K]

Let x=length of king cobra
Let y=length of black mamba

x=118
y=x-22
y=118-22
y=96
Therefore black mamba has an average length of 96 inches

8 0

3 years ago

Solve: 0.1m−1.3m=−2.1−2.7.

mars1129 [50]

Answer:4

Step-by-step explanation:

Simplify what you can which is 0.1m-1.3m

you end up getting -1.2m

Now do the other side of the equation which is 2.1-2.7 which is -4.8

Divide -4.8 by -1.2 to get m=4

3 0

3 years ago

Read 2 more answers

Whats the GCF of 15 and 35 and 70

Andrej [43]

Just think what do all the numbers have in common? What number can relate to all of them and is the largest number? That's how you find GCF, straight of the bat I can see that the GCF is 5 because nothing higher than five can match up to all of them, in other words nothing other than 5 or higher than 5 is a factor of all the numbers.

4 0

3 years ago

John has a $2, $1, $0.50, $0.25, $0.10, and $0.05 coin in his pocket. How many different sums of money can he make?

Paladinen [302]

Answer:

64

Step-by-step explanation:

the different sum of money is 64

3 0

3 years ago