Question

A wall clock strikes the bell once at 1 o’clock, 2 times at 2 o’clock, 3 times at 3 o’clock and so on. How many times will it strike in a particular day? Find the standard deviation of the number of strikes the bell make a day.

Answer 1

Wall clock strikes the bell in 12 hours

1, 2, 3, 4, 5, …, 12

Wall clock strikes in a day  ...(24 hours)

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24.

Assumed mean = 14

xi	di = xi − A = xi − 14	di2
2	12	144
4	− 10	100
6	− 8	64
8	− 6	36
10	− 4	16
12	− 2	4
14	0	0
16	2	4
18	4	16
20	6	36
22	8	64
24	10	100
n = 12	`sum"d"_"i"` = − 12	`sum"d"_"i"^2` = 584

Here n = 12, `sum"d"_"i"` = − 12, `sum"d"_"i"^2` = 584

Standard deviation = `sqrt((sum"d"_"i"^2)/"n" - ((sum"d"_"i")/"n")^2`

= `sqrt(584/12 - (- 12/12)^2`

= `sqrt(48.67 - 1)`

= `sqrt(47.67)`

= 6.904

= 6.9

Standard deviation of the bell strike in a day = 6.9

Aliter:

A wall clock strikes in a day is 2, 4, 6, 8, 10, 12, ..., 24

2 [1 + 2 + 3 + 4 + 5 ... + 12]

Standard deviation for "n" natural number is (S.D.)

= `sqrt(("n"^2 - 1)/12)`

= `2sqrt((12^2 - 1)/12)`

= `2sqrt((144 - 1)/12)`

= `2sqrt(11.9166)`

= 2 × 3.45

= 6.9

The standard deviation of bell strike in a day is 6.9