The number of checks encashed each day at the five branches of Citizens’ Bank during the past month had the following frequency distribution:

Class Frequency

0-199 10

200-399 13

400-599 17

600-799 42

800-999 18

The Bank Manager is worried about the imbalance in work load causing staffing problem whenever the standard deviation exceeds 200 cheques. Ascertain whether the manager’s concern holds any ground.

### 1 Answer | Add Yours

`x_1=(0+199)/2=99.5`

`...`

`...`

`...`

`x_5=(800+999)/2=899.5`

`sum_(i=1)^5f_i=100`

`sum_(i=1)^5f_ix_i=58950`

`sum_(i=1)^5f_i(x_i-barx)=5870000`

where `barx` is mean and equal to

`barx=(sum_(i=1)^nf_ix_i)/(sum_(i=1)^5f_i)`

`=58950/100=589.50`

`sigma^2=(sum_(i=1)^5f_i(x_i-barx)^2)/(sum_(i=1)^5f_i)`

`sigma^2=5870000/100`

`` Let mean not change .

apply ' t ' test for the hypotheise of manager.

`t_{cal}=(barxsqrtd)/sigma` ,

where d=5-1=4

`t_(cal)=(589.50xxsqrt(4))/242.28`

`=4.8662`

`t_(tab)=2.132`

t_ tab= table value

table value is less than calculated value

so hypothesis is insignificant.

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