Question

The number of arrivals per minute at a bank located in the central business district of a large city was recorded over a period of 200​ minutes, with the results shown in the table below. Complete​ (a) through​ (c) to the right.

Arrivals   Frequency
0   21
1   41
2   43
3   37
4   25
5   17
6   9
7   5
8   2

a. Compute the expected number of arrivals per minute.
μ=___( please type as an integer or a decimal)

b. Compute the standard deviation
σ=___(please round to three decimal places as needed

c. What is the probability that there will be fewer than 2 arrivals in a given minute?

(Type an integer or decimal rounded to three decimal places as needed.)

Answer 1

Dividing each value with total frequency of 200:

x	P(X=x)	xP(x)	x2P(x)
0	0.105	0.00000	0.00000
1	0.205	0.20500	0.20500
2	0.215	0.43000	0.86000
3	0.185	0.55500	1.66500
4	0.125	0.50000	2.00000
5	0.085	0.42500	2.12500
6	0.045	0.27000	1.62000
7	0.025	0.17500	1.22500
8	0.010	0.08000	0.64000
total		2.6400	10.3400
	E(x) =μ=	ΣxP(x) =	2.6400
	E(x2) =	Σx2P(x) =	10.3400
	Var(x)=σ2 =	E(x2)-(E(x))2=	3.370400
	std deviation=	σ= √σ2 =	1.83586

a)

μ= 2.64

b)

σ= 1.836

c)probability that there will be fewer than 2 arrivals in a given minute =0.310