Answer to Question #234905 in Statistics and Probability for Muhammad bilal

Question

b. From past experience, it is known that the number of tickets purchased by a student standing in line at the ticket window for the cricket match of IU(main) against IU(North) follows a distribution that has mean µ = 2.5 and standard deviation σ = 2.1. Suppose that few hours before the start of one of these matches there are 100 eager students standing in line to purchase tickets. If only 249 tickets remain, what is the probability that all 100 students will be able to purchase the tickets they desire? c. The amount of regular unleaded gasoline purchased every week at a gas station near City station follows the normal distribution with mean 45000 gallons and standard deviation 10000 gallons. The starting supply of gasoline is 75000 gallons, and there is a scheduled weekly delivery of 48000 gallons. Find the probability that, after 14 weeks, the supply of gasoline will be below on 20000 gallons. 

Answer 1

b. Let $X=$ the number of tickets purchased by a student : $X\sim N(\mu, \sigma^2).$

Given $\mu=2.5, \sigma=2.1.$

$$P(X\leq2.49)=P(Z\leq\dfrac{2.49-2.5}{2.1})\approx P(Z\leq0.004762)$$

$$\approx P(Z\leq0.004762)\approx0.5019$$

c.

$$75000+14(48000)-20000=727000$$

Let $X=$ the amount of regular unleaded gasoline purchased 14 week: $X\sim N(14\mu, 14\sigma^2)$

Given $\mu=45000, \sigma=10000.$

$$P(X>727000)=1-P(X\leq727000)$$

$$=1-P(Z\leq\dfrac{727000-14(45000)}{10000\sqrt{14}})$$

$$\approx1-P(Z\leq2.592434)\approx 0.004765$$

The probability that, after 14 weeks, the supply of gasoline will be below on 20000 gallons is  

$0.004765.$