Question

The answers are in red. Please do part a-f, Thanks in advance :)

Assume the time required to pass through security at a particular airport follows the continuous uniform distribution with a minimum time of 10 minutes and maximum time of 36 minutes. Complete parts (a) through (f) below. a) Calculate the value of f(x). f(x) = 0.038 (Type an integer or decimal rounded to three decimal places as needed.) b) What are the mean and standard deviation for this distribution? The mean of this distribution is 23 minutes. (Type an integer or a decimal.) The standard deviation of this distribution is 7.51 minutes. Type an integer or decimal rounded to two decimal places as needed.) c) What is the probability that the next passenger will require less than 29 minutes to pass through security? 0.731 (Type an integer or decimal rounded to three decimal places as needed.) d) What is the probability that the next passenger will require more than 24 minutes to pass through security? 0.462 (Type an integer or decimal rounded to three decimal places as needed.) e) What is the probability that the next passenger will require between 14 and 21 minutes to pass through security? 0.269 (Type an integer or decimal rounded to three decimal places as needed.) f) What time represents the 75th percentile of this distribution? 29.5 minutes (Type an integer or a decimal.)

Answer 1

solution f(x) = bra (M)=bae actor (numitorm loo[a, b] a = 10 0.038 b=36 b) Mean = atb - 10+36 = [23] stondend dari ben 160 g40,- no pot. Jude c) Standard deviation = (b. V 2 = 7:51] 34 36 36 tos 24 2-4 da 26-24 16.26 T 0.462 tico Pooblom moc P(+229) P(x229) 29-10 dx = 29-10 - 10.42] (e) P(19LXL2) 21-14 26 a 0. 269 H) Plecxo) = 0.75 tida = 0.75 » X0-10 = 0.75 » Xo = 29.57