Find the value of Wif A=LW, A = 70 m2, and L = 5 m.

A company services home air conditioners. It is known that times for service calls follow a normal distribution with a mean of 7

SCORPION-xisa [38]

Answer:

The probability that exactly eight of them take more than 93.6 minutes is 5.6015 $\times 10^{-6}$ .

Step-by-step explanation:

We are given that it is known that times for service calls follow a normal distribution with a mean of 75 minutes and a standard deviation of 15 minutes.

A random sample of twelve service calls is taken.

So, firstly we will find the probability that service calls take more than 93.6 minutes.

Let X = times for service calls.

So, X ~ Normal( $\mu=75,\sigma^{2} =15^{2}$ )

The z-score probability distribution for the normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = mean time = 75 minutes

$\sigma$ = standard deviation = 15 minutes

Now, the probability that service calls take more than 93.6 minutes is given by = P(X > 93.6 minutes)

P(X > 93.6 min) = P( $\frac{X-\mu}{\sigma}$ > $\frac{93.6-75}{15}$ ) = P(Z > 1.24) = 1 - P(Z $\leq$ 1.24)

= 1 - 0.8925 = 0.1075

The above probability is calculated by looking at the value of x = 1.24 in the z table which has an area of 0.8925.

Now, we will use the binomial distribution to find the probability that exactly eight of them take more than 93.6 minutes, that is;

$P(Y = y) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; y = 0,1,2,3,.........$

where, n = number of trials (samples) taken = 12 service calls

r = number of success = exactly 8

p = probability of success which in our question is probability that

it takes more than 93.6 minutes, i.e. p = 0.1075.

Let Y = Number of service calls which takes more than 93.6 minutes

So, Y ~ Binom(n = 12, p = 0.1075)

Now, the probability that exactly eight of them take more than 93.6 minutes is given by = P(Y = 8)

P(Y = 8) = $\binom{12}{8}\times 0.1075^{8} \times (1-0.1075)^{12-8}$

= $495 \times 0.1075^{8} \times 0.8925^{4}$

= 5.6015 $\times 10^{-6}$ .

6 0

3 years ago

HELP PLEASE? What is the coefficient of y in expansion of (y+4)^4 ?

gulaghasi [49]

256.

The coefficient of just the y term would be 256 because the entire expanded equation looks like this:

y^4+16y^3+96y^2+256y+256

3 0

4 years ago

Write an expression for the sequence of operations described below.

Leokris [45]

Answer:

$9+\dfrac{4}{8}$

Step-by-step explanation:

The quotient of 4 and 8 is ...

$\dfrac{4}{8}$

To increase 9 by that amount, you have to add that amount to 9:

$9+\dfrac{4}{8}$

6 0

3 years ago

Using factor theorem factorise each of the following

yuradex [85]

Answer:

(x + 1)(x - 1) (x- 2)(x - 5)

Step-by-step explanation:

Solving in steps:

x^4 - 7x^3 + 9x² + 7 x – 10=
(x^4 - 1 )- (7x^3 - 7x) + (9x^2 - 9) =
(x^2 + 1)(x^2 - 1) - 7x(x^2 - 1) + 9(x^2 - 1) =
(x^2-1)(x^2 + 1 - 7x + 9) =
(x + 1)(x - 1)(x^2 - 7x + 10) =
(x + 1)(x - 1)((x^2 - 2x) - (5x - 10)) =
(x + 1)(x - 1) (x- 2)(x - 5)

8 0

3 years ago

Write a function rule for each table.

Nat2105 [25]

Let's assume that this function is linear.

Take any 2 of the points and find the slope of the line segment connecting them:

103 - 80
m = ------------- = 23, meaning $23 per day. Subtracting $23 from $34 (in the table), we get $11. Thus, the correct linear relationship is B.
4 - 3

6 0

3 years ago

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