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   25
1   55
2   36
3   31
4   23
5   17
6   8
7   4
8   1

Compute the expected number of arrivals per minute.

mean=

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

b. Compute the standard deviation.

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

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

P(x<2)=

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

Answer 1

number of arrivals(X)	frequency (F)	P(x)=F /n	x*P(x)	x2*P(x)
0	25	0.125	0	0
1	55	0.275	0.275	0.275
2	36	0.18	0.36	0.72
3	31	0.155	0.465	1.395
4	23	0.115	0.46	1.84
5	17	0.085	0.425	2.125
6	8	0.04	0.24	1.44
7	4	0.02	0.14	0.98
8	1	0.005	0.04	0.32
	sum(n)= 200		sum=2.405	sum=9.095

a). the expected number of arrivals per minute be:-

Σx*P(X) = 2.405

b). the standard deviation be:-

= √9.095-2.4052

= 1.8196

c). the probability that there will be fewer than 2 arrivals in a given minute be:-

= 0.125 + 0.275

= 0.4

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