Mathematics, 08.04.2020 03:27 Galycon12

Births are approximately Uniformly distributed between the 52 weeks of the year. They can be said to follow a Uniform distribution from 1 to 53 (a spread of 52 weeks). Round answers to 4 decimal places when possible a. The mean of this distribution is born at the exact moment that week 36 begins is Px 36) between weeks 8 and 45 is P(8 < ®?45)- The probability that a person will be born after week 16 is P(x > b. The standard deviation is c. The probability that a person will be d. The probability that a person will be born h. Find the minimum for the lower f. P(x>201 x 46). Find the 48th percentile quartile.

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Answer from: babyboo6745

(a) The mean of the distribution of births between the 52 weeks of a year is 27.

(b) The standard deviation of the distribution of births between the 52 weeks of a year is 15.01.

(d) The probability that a person will be born between weeks 8 and 45 is 0.7115.

(e) The probability that a person is born after week 16 is 0.7115.

Step-by-step explanation:

The random variable X can be defined as the births between the 52 weeks of the year.

The random variable X is uniformly distributed with parameters a = 1 to b = 53.

The probability distribution function of X is:

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

(a)

Compute the mean of the Uniformly distributed random variable X as follows:

$E(X)=\frac{1}{2}(a+b)$

$=\frac{1}{2}\times (1+53)$

=27

Thus, the mean of the distribution of births between the 52 weeks of a year is 27.

(b)

Compute the standard deviation of the Uniformly distributed random variable X as follows:

$SD(X)=\sqrt{\frac{1}{12}\times (b-a)^{2}}$

$=\sqrt{\frac{1}{12}\times (53-1)^{2}}$

=15.01

Thus, the standard deviation of the distribution of births between the 52 weeks of a year is 15.01.

(c)

Compute the probability that a person is born exactly at the beginning of week 36 as follows:

Use continuity correction.

P (X = 36) = P (36 - 0.5 < X < 36 + 0.5)

= P (35.5 < X < 36.5)

$=\int\limits^{36.5}_{35.5}{\frac{1}{53-1}}}\, dx\\$

$=\frac{1}{52}\times \int\limits^{36.5}_{35.5}{1}\, dx$

$=\frac{36.5-35.5}{52}$

=0.0192

Thus, the probability that a person is born exactly at the beginning of week 36 is 0.0192.

(d)

Compute the probability that a person will be born between weeks 8 and 45 as follows:

P(8

$=\frac{1}{52}\times \int\limits^{45}_{8}{1}\, dx$

$=\frac{45-8}{52}$

=0.7115

Thus, the probability that a person will be born between weeks 8 and 45 is 0.7115.

(e)

Compute the probability that a person is born after week 16 as follows:

$P(X16)=\int\limits^{53}_{16}{\frac{1}{53-1}}\, dx$

$=\frac{1}{52}\times \int\limits^{53}_{16}{1}\, dx$

$=\frac{53-16}{52}$

=0.7115

Thus, the probability that a person is born after week 16 is 0.7115.

Answer from: Quest

why can't you?

step-by-step explanation:

Answer from: Quest

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17. e. none of the above

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