Question

8. A swimming pool is filled at a rate that is uniformly distributed between 20 and 26.3 gallons per minute. a. Draw a sketch that illustrates this particular situation. Please label all relevant information for this probability density function. (5 pts) b. What is the probability that the filling rate at any one time is between 21.3 and 24.6 gallons per minute? (6 pts) c. What is the median rate at which this swimming pool is filled? (4 pts) 8. (continued) d. What is the standard deviation of the rate at which this pool is filled? (4 pts) e. Suppose the pool attendant was certain that the rate was at least 22 gallons per minute, what is the probability that the average filling rate exceeded 25 gallons per minute? (6 pts)

Answer 1

6 now consider Probability that the filling rate at any one time Es between 21.3 and 24-6 gallons per minerte = P( 21-3 < x < 24.6) ) *P(21.35 x 5 24.6) -- plx=246) - P(x < 21:3) 3 .3 ł 0.52381 Б-а ( ? 6 if x, Elaub] Required probability =P(2135 X5 24 6) = 0.5238)

- we know that, In Unifom Distribution, x ~ Unit (a,b) Median, an-Ź (a+b) i teel, xn Unit ( 20, 26.3) & Median, am = √ (20 +26. 3) = 2 (463) - 2315 Median = 23-15 gallone paminu t for xn Unit (a,b) - Standard deviation, o a less po (26-3-20)2 = (6-a)2 (6.3)+V3.3095 - 1-8187 i letandard standard de deviation = 1.8187. gallons per minute

CP(x2) ut ba @ Guren, rate was atleast 22 gallone peeninute, then probability that average filling rate exceeded 25 gallons per minute = P(x725/x222) = ? ale Plx220/X222) = P(x=25 and *222) 2 P(x222) - P(x=25) -- P(x225) - P(x222) - P(x(22) (22-20 1-03:22) 1-630 26-3-20 6-3-5 - 1-3 cSE0.3024 - 3 20.30 - Q3 6.3-2 . 4.3 ...pfx>250x222) = 0,3024