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u ptsBirths are approximately Uniformly distributed between the 52 weeks of the year. They can be saidto follow a Uniform distribution from 1 to 53 (a spread of 52 weeks). Round answers to 4 decimalplaces when possible.a. The mean of this distribution isb. The standard deviation isC. The probability that a person will be born at the exact moment that week 18 begins isP(x = 18) =d. The probability that a person will be born between weeks 10 and 43 isP(10 < x < 43) =e. The probability that a person will be born after week 35 isP(x > 35)f. P(x > 18 x < 32) =g. Find the 47th percentile.h. Find the minimum for the upper quarter.

U PtsBirths Are Approximately Uniformly Distributed Between The 52 Weeks Of The Year They Can Be Saidto Follow A Uniform Distribution From 1 To 53 A Spread Of 5 class=

Sagot :

Step 1

A) The mean distribution

[tex]\frac{1+53}{2}=\frac{54}{2}=27.0000[/tex]

Step 2

B) The standard deviation

[tex]\begin{gathered} SD=\sqrt[]{\frac{1}{12}\times(b-a)^2} \\ SD=\sqrt[]{\frac{1}{12}(53-1)^2} \\ SD=\text{ }15.0111 \end{gathered}[/tex]

Step 3

C)

[tex]P(x=18)=0[/tex]

Step 4

D)

[tex]\begin{gathered} P(10Step 5

E)

[tex]P(x>35)=\text{ }\frac{53-35}{52}=\frac{18}{52}=0.3462[/tex]

Step 6

F)

[tex]P(x>18|x<32)=\text{ }\frac{32-18}{32-1}=\frac{14}{31}=0.4516[/tex]

Step 7

G)

[tex]\begin{gathered} \text{The 47th percentile}=1\text{ + }\frac{47}{100}(53-1)_{} \\ =1+0.47(52)=25.44_{}00 \end{gathered}[/tex]

Step 8

[tex]\begin{gathered} \text{The minimum for the upper percentile = 1+((}\frac{3}{4})(53^{}-1) \\ =1+0.75(52) \\ =1+\text{ 39=40}.0000 \end{gathered}[/tex]

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