Tracy and Diane, working as twohairstylists at coiffeur, dress hair of women at a rate of 3 women per hour. The hairdressing time for Tracy and Dianeis exponentially distributed. Women arrive to the coiffeur according to a Poisson distribution with a rate of 5 per hour.a) What is the probability that Tracy is busy? b) What is the probability that Diane is idle? c)On average, how many women are waiting for hairdressing? d)On average, how long must a woman wait before hairdressing begins? e) What is the average time a woman spends in the coiffeur? f) Find the probability that a woman’s waiting time in the coiffeur is more than 90 minutes?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Tracy and Diane, working as twohairstylists at coiffeur, dress hair of women at a rate of 3 women per hour. The hairdressing time for Tracy and Dianeis exponentially distributed. Women arrive to the coiffeur according to a Poisson distribution with a rate of 5 per hour.a) What is the probability that Tracy is busy?
b) What is the probability that Diane is idle?
c)On average, how many women are waiting for hairdressing?
d)On average, how long must a woman wait before hairdressing begins?
e) What is the average time a woman spends in the coiffeur?
f) Find the probability that a woman’s waiting time in the coiffeur is more than 90 minutes?
Note:-We’ll answer the first three subparts of the question since the exact one wasn’t specified. Please submit a new question specifying the one you’d like answered.
Given data
Arrival rate = 3 women per hour
Service rate = 5 women per hour
Ans A:
The probability that Tracy is busy
Thus, the probability that Tracy is busy is 0.6
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