MATH 118: Statistics and Probability Homework #3 solved

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Problem 1: (15+20=35 points)
Kuru Kahveci Mehmet Efendi (the producer), which is a coffee brand, supplies coffee beans to a coffee shop
(the consumer) in Kadikoy. The coffee is supplied as 50 packages at each order and each package has 1 kg coffee
beans. The consumer regards an order as acceptable provided that there are not more than 5 packages which
have stale coffee beans. Rather than test all packages in the order, 10 packages are selected at random and
tested.
(a) Find the probability that out of a sample of 10, d = 0, 1, 2, 3, 4, 5 are stale when there are actually 5 stale
packages in the order.
(Solution)
(b) Suppose that the consumer will accept the order provided that not more than m stale packages are found
in the sample of 10.
• Find the probability that the order is accepted when there are 5 stale packages in the order.
(Solution)
• Find the probability that the order is rejected when there are 3 stale packages in the order.
(Solution)
1
– Homework #3 2
Problem 2: (20+5=25 points)
Hairdresser and barber shops reopened in Turkey under strict hygiene rules after almost two months at the
11th of May. Regarding to ”new normal” rules, the number of customers arriving per hour at a hairdresser
should be under control by the owner of the hairdresser shop. The hairdresser can accept at most 4 customers
per hour with its conditions. Before arranging appointments with the customers, the owner wants to estimate
whether there can be more demands than the owner can accept. The number of customers arriving per hour is
assumed to follow a Poisson distribution with mean λ = 6.
(a) Compute the probability that more than 12 customers will arrive in a 3-hour period.
(Solution)
(b) What is the mean number of arrivals during a 3-hour period?
(Solution)
Problem 3: (8+8+8+8+8=40 points)
Given a normal distribution with µ = 35 and σ = 7, find
(a) the normal curve area to the right of x = 21.
(Solution)
(b) the normal curve area to the left of x = 25.
(Solution)
(c) the normal curve area between x = 32 and x = 41.
(Solution)
(d) the value of x that has 60% of the normal curve area to the left.
(Solution)
(e) the two values of x that contain the middle 75% of the normal curve area.
(Solution)