Let "X=" the number of minutes a customer rents the bike in minutes: "X\\sim N(\\mu,\\sigma^2)."
Then
Given that "\\mu=75\\ minutes, \\sigma=15\\ minutes."
(a) What proportion of customers would rent the bike for more than 2 hours?
(b) There are 9% customers would rent the bike for less than K minutes. What is the value of K?
(c) What are the (i) mean, (ii) median, (iii) variance, and (iv) standard deviation of the rental fee paid by a customer?
"(i) \\ \\ mean=\\$10+\\$0.5\\cdot75=\\$47.50,"
"(ii) \\ \\ median=mean=\\$47.50,"
"(iii)Variance=(0.5)^2(15)^2=56.25,"
"(iv) Standard\\ deviation=\\sqrt{Variance}=\\sqrt{56.25}=\\$7.50"
(d) Suppose (L1, L2) indicates the 90% symmetric range around the mean rental fee paid by a customer. What are the values of L1 and L2 respectively?
"\\delta\\approx1.644852\\cdot7.5\\approx12.3364"
"L_1=\\mu-\\delta\\approx47.50-12.34=35.16"
"L_2=\\mu+\\delta\\approx47.50+12.34=59.84"
"L_1=\\$35.16, L_2=\\$59.84"
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