Can someone teach me how to answer all the questions as mentioned above? 5. On a

Question

Can someone teach me how to answer all the questions as mentioned above?

5. On average, six people per hour use an electronic teller machine during the prime shopping hours in a department store. What is the probability that no one will use the facility during a five minutes interval? (4 marks) The lifetime of an electrical component is known to follow a normal distribution witha mean 200 hours and a standard deviation 19 hours. What is the probability that a randomly selected component will last 6. (a) more than 220 hours? (3 marks) (b) between 200 and 240 hours? (2 marks) A random sample of 200 adults was taken, and they were asked whether they prefer watching news or documentary on television. Out of those people, 120 are male and 80 of males prefer news. 50 of the females prefer documentary. If an adult is selected at random from this group, find the probability that this adult 7. (a) is a female (1 mark) (b) is a male given he prefers news. (3 marks) (c) prefers documentary given she is a female (3 marks) (d) is a male or prefers news (2 marks)

Explanation / Answer

Ans:

5)Poisson distribution:

rate=6 per hr=0.1 per min

So,for 5 minute interval,there will be on average 0.1*5=0.5 person

P(x=k)=e-0.5*(0.5k/k!)

P(no one will use facility)=P(x=0)=e-0.5*(0.50/0!)=e-0.5=0.6065

6)Given that

mean=200

standard deviation=19

a)

z=(220-200)/19=1.053

P(z>!.053)=1-P(z<=1.053)=1-0.8538=0.1462

b)

z score for 200,

z=(200-200)/19=0

z score for 240.

z=(240-200)/19=2.105

P(0<=z<=2.105)=P(z<=2.105)-P(z<=0)=0.9824-0.5=0.4824

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