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

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.         

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`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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