In a well known hotel in Rajkot, the average time to serve food to a family is 6 minutes. It follows exponential distribution. Find the probability that A family will take time between 4 and 5 minutes to get the food
Answers
Answer:
Let X = amount of time (in minutes) a postal clerk spends with his or her customer. The time is known to have an exponential distribution with the average amount of time equal to four minutes.
X is a continuous random variable since time is measured. It is given that μ = 4 minutes. To do any calculations, you must know m, the decay parameter.
m=\frac{1}{\mu }. Therefore, m=\frac{1}{4}=0.25.
The standard deviation, σ, is the same as the mean. μ = σ
The distribution notation is X ~ Exp(m). Therefore, X ~ Exp(0.25).
The probability density function is f(x) = me–mx. The number e = 2.71828182846… It is a number that is used often in mathematics. Scientific calculators have the key “ex.” If you enter one for x, the calculator will display the value e.
The curve is:
f(x) = 0.25e–0.25x where x is at least zero and m = 0.25.
For example, f(5) = 0.25e(-0.25)(5) = 0.072. The value 0.072 is the height of the curve when x = 5. In (Figure) below, you will learn how to find probabilities using the decay parameter.
The graph is as follows:
Exponential graph with increments of 2 from 0-20 on the x-axis of μ = 4 and increments of 0.05 from 0.05-0.25 on the y-axis of m = 0.25. The curved line begins at the top at point (0, 0.25) and curves down to point (20, 0). The x-axis is equal to a continuous random variable.
Notice the graph is a declining curve. When x = 0,
f(x) = 0.25e(−0.25)(0) = (0.25)(1) = 0.25 = m. The maximum value on the y-axis is m.
Step-by-step explanation:
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