Given the weight of a man has a normal distribution with a mean of 75 kg and a standard deviation of 10 kg. (i) Find the probability of a randomly selected man, his weight is greater than 80 kg. (ii) 5% of the men are having weight more than k kg. Find the value of k. (iii) If 20 different men arc randomly sclccted, find the probability that thcir mcan weight is less than 70 kg.

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Given the weight of a man has a normal distribution with a mean of 75 kg and a standard
deviation of 10 kg.
(i)
Find the probability of a randomly selected man, his weight is greater than 80 kg.
(ii)
5% of the men are having weight more than k kg. Find the value of k.
If 20 different men arc randomly sclccted, find the probability that thcir mcan weight
is less than 70 kg.
(iii)
d)
Suppose that the number of demands for taxis to a taxi firm follows a Poisson distribution
with a mean of 5 demands in every 30 minutes. Find the probability that there are at most 2
demands in 15 minutes.
Transcribed Image Text:Given the weight of a man has a normal distribution with a mean of 75 kg and a standard deviation of 10 kg. (i) Find the probability of a randomly selected man, his weight is greater than 80 kg. (ii) 5% of the men are having weight more than k kg. Find the value of k. If 20 different men arc randomly sclccted, find the probability that thcir mcan weight is less than 70 kg. (iii) d) Suppose that the number of demands for taxis to a taxi firm follows a Poisson distribution with a mean of 5 demands in every 30 minutes. Find the probability that there are at most 2 demands in 15 minutes.
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