Mathematics, 17.08.2020 17:01 030702princessjs

The time for service call follows a uniform distribution over the interval 20 to 60 minutes. 1. What is the probability that the service call takes longer than 30 minutes?
2. What is the interquartile range?
3. What is the 90th percentile?

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Answer from: kolibeilfuss

(1) 0.75

(2) 30

(3) 56

Step-by-step explanation:

Let X represent the time for service call.

It is provided that: $X\sim Uni(20, 60)$

The probability density function of X is:

$f_{X}(x)=\frac{1}{b-a};\ a$

(1)

Compute the probability that the service call takes longer than 30 minutes as follows:

$P(X30)=\int\limits^{60}_{30} {\frac{1}{60-20}} \, dx$

$=\frac{1}{40}\times |x|^{60}_{30}\\\\=\frac{60-30}{40}\\\\=\frac{3}{4}\\\\=0.75$

Thus, the probability that the service call takes longer than 30 minutes is 0.75.

(2)

The Inter quartile range is the difference between the 75th and 25th percentile.

From part (1), we know that P (X > 30) = 0.75.

⇒ 1 - P (X > 30) = 0.75

⇒ P (X < 30) = 0.25

The 25th percentile is 30.

Compute the 75th percentile as follows:

P(X

The 75th percentile is 50.

Then the inter quartile range is:

$IQR=P_{75}-P_{25}$

$=50-20\\=30$

Thus, the inter quartile range is 30.

(3)

Compute the 90th percentile as follows:

P(X

The 90th percentile is 56.

Answer from: Quest

29.5977692753

step-by-step explanation:

Answer from: Quest

the most boring thing ever written

step-by-step explanation:

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