Number 11 thanks ASAP ASAP

kotykmax [81]

I found out it is m = 91 if it helps

7 0

3 years ago

Geologists estimate the time since the most recent cooling of a mineral by counting the number of uranium fission tracks on the

Oliga [24]

Answer:

(a) The value of P (X = 7) is 0.1388.

(b) The value of P (X ≥ 3) is 0.9380.

(c) The value of P (2 < X < 7) is 0.5433.

(d) $\mu_{X}=6$

(e) $\sigma_{X}=2.45$

Step-by-step explanation:

Let X = number of uranium fission tracks on per cm² surface area of the mineral.

The average number of track per cm² surface area is, λ = 6.

The random variable X follows a Poisson distribution with parameter λ = 6.

The probability mass function of a Poisson distribution is:

$P(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!};\ x=0, 1, 2, 3...$

(a)

Compute the value of P (X = 7) as follows:

$P(X=6)=\frac{e^{-6}(6)^{7}}{7!}=\frac{0.0025\times 279936}{5040}=0.1388$

Thus, the value of P (X = 7) is 0.1388.

(b)

Compute the value of P (X ≥ 3) as follows:

P (X ≥ 3) = 1 - P (X < 3)

= 1 - P (X = 0) - P (X = 1) - P (X = 2)

$=1-\frac{e^{-6}(6)^{0}}{0!}-\frac{e^{-6}(6)^{1}}{1!}-\frac{e^{-6}(6)^{2}}{2!}\\=1-0.00248-0.01487-0.04462\\=0.93803\\\approx0.9380$

Thus, the value of P (X ≥ 3) is 0.9380.

(c)

Compute the value of P (2 < X < 7) as follows:

P (2 < X < 7) = P (X = 3) + P (X = 4) + P (X = 5) + P (X = 6)

$=\frac{e^{-6}(6)^{3}}{3!}+\frac{e^{-6}(6)^{4}}{4!}+\frac{e^{-6}(6)^{5}}{5!}+\frac{e^{-6}(6)^{6}}{6!}\\=0.08924+0.13385+0.16062+0.16062\\=0.54433\\\approx0.5443$

Thus, the value of P (2 < X < 7) is 0.5433.

(d)

The mean of the Poisson distribution is:

$\mu_{X}=\lambda=6$

(e)

The standard deviation of the Poisson distribution is:

$\sigma_{X}=\sqrt{\sigma^{2}_{X}}=\sqrt{\lambda}=\sqrt{6}=2.4495\approx2.45$

5 0

4 years ago

Monte performs an experiment using 2 identical graduated cylinders, each with a radius of 2 cm. The volume of the liquid in the

Thepotemich [5.8K]

The difference in volume is 125.6 cm^3, so the difference in height will be
.. 125.6 cm^3/(3.14*(2 cm)^2) = 10 cm

5 0

3 years ago

Andrew has a balance of $6,000 on his credit card with an annual interest rate of 12%. To pay off the $6,000 in three years, And

amid [387]

Answer:

$1,174.44

Step-by-step explanation:

- Three year period will have 36 payments, then the total payment is $7,174.44

- In which $6,000 is the balance of credit card at beginning

- The total interest paid over the 03 years is $1,174.44 = $7,174.44 - $6,000

5 0

3 years ago

Ron Co. sold sweatshirts ($20) and baseball caps ($10). If total sales were $2,860 and people bought 6 times as many sweatshirts

NISA [10]

It's been answered at brainly.com/question/4030336

6 0

3 years ago