Answer:
(a) 3.55
(b) 3.45 and 1.86
(c) 0.25
(d) 0.016
Step-by-step explanation:
The random variable <em>X</em> denotes the number of people in a group (party) at a restaurant.
(a)
The formula to compute the mean is:
Consider the Excel sheet attached.
The mean is, 3.55.
(b)
The formula to compute the variance is:
Consider the Excel sheet attached.
Compute the variance as follows:
The variance is, 3.45.
Compute the standard deviation as follows:
The standard deviation is, 1.86.
(c)
Compute the probability that the next party will be over 4 people as follows:
Thus, the probability that the next party will be over 4 people is 0.25.
(d)
Compute the probability that the next three parties will each be over 4 people as follows:
It is provided that the three parties are independent.
P (Next 3 parties will be each over 4) = [P (X > 4)]³
Thus, the probability that the next three parties will each be over 4 people is 0.016.