Ayeud 1123, MS. Syuley McNTICKS HOIUS

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

4 years ago

Plz help will give branliest !!!!!!!!!

vaieri [72.5K]

Answer24:

Step-by-step explanation:

It is the answer

4 0

3 years ago

I need the volume of these two figures

Lesechka [4]

Answer: Part A 11520 for the blue one

Part B for the orange one is 12

Step-by-step explanation:

Multiply them all by each other

3 0

3 years ago

(NEED HELP ASAP)

denis-greek [22]

Pick any value in the y column of the table. I'm going to pick 81. Divide the value you picked by the previous y value, which in my case would be 9

Dividing the values gives: 81/9 = 9

So the base is 9. We multiply each y value by 9 to get the next y value
Eg: to go from 1/81 to 1/9, we multiply by 9. Same for 1/9 to 1, and so on.

Answer: Choice B) 9

Note: This trick only works because x is increasing by 1 each time

8 0

4 years ago

If you roll two number cubes, what is the probability of their sum being equal to a value of seven or higher?

rodikova [14]

If the cubes are die such that each face has numbers from 1 to 6. Rolling two of them, there are 6x6 or 36 ways in which they may be arranged. For their numbers to sum to 7, the numbers should be 1 and 6, 2 and 5, 2 and 6, 3 and 4, 3 and 5, 3 and 6, 4 and 3, 4 and 4, 4 and 5, 4 and 6, 5 and 2, 5 and 3, 5 and 4, 5 and 5, 5 and 6, 6 and 1, 6 and 2, 6 and 3, 6 and 4, 6 and 5, 6 and 6. All in all there are 21 out of 36 and the probability is equal to 7/12.

3 0

3 years ago

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