The table shows the scores obtained when a fair die was thrown a number of times. If the probability of obtaining a 3 is 0.26, find the (a) median (b) standard deviation of the distribution.

Monday, 14 April 2025

The table shows the scores obtained when a fair die was thrown a number of times. If ...

Trending Questions

** Free JAMB 2025 CBT Practice **

Take Free Practice Test On 2025 JAMB UTME, Post UTME, WAEC SSCE, GCE, NECO SSCE

The table shows the scores obtained when a fair die was thrown a number of times.

Score	1	2	3	4	5	6
Frequency	2	5	x	11	9	10

If the probability of obtaining a 3 is 0.26, find the (a) median
(b) standard deviation of the distribution.

Explanation

Score	1	2	3	4	5	6
Frequency	2	5	x	11	9	10

P(3) = 0.26

\frac{x}{37 + x} = 0.26

x = 0.26 (37 + x) ⟹ x = 9.62 + 0.26 x

x - 0.26 x = 9.62 ⟹ 0.74 x = 9.62

x = \frac{9.62}{0.74} = 13

Total toss frequency = 37 + x
= 37 + 13
= 50.
(a) Median =

\frac{n + 1}{2}

\frac{50 + 1}{2}

= 25.5
From the table, 25.5 occurs at 4 which is the median.
(b) Standard deviation =

\sqrt{\frac{\sum f d^{2}}{\sum f}}

$x$	$f$	$\fx$	$d = \| x - \bar{x} \|$	$d^{2}$	$f d^{2}$
1	2	2	-3	9	18
2	5	10	-2	4	20
3	13	39	-1	1	13
4	11	44	0	0	0
5	9	45	1	1	9
6	10	60	2	4	40
$\sum$	50	200			100

M e a n (\bar{x}) = \frac{\sum f x}{\sum f}

\frac{200}{50} = 4 S . D = \(\sqrt{\frac{100}{50}}

\sqrt{2}

= 1.4142

Prev Current Next

STAY UPDATED
FOLLOW US ON :

Facebook

Subjects

• Accounts - Principles of Accounts

• Christian Religious Knowledge (CRK)

• Islamic Religious Knowledge (IRK)

All Views, Names, Acronyms, Trademarks, Expressed on this website are those of their respective owners. Please note that www.schoolngr.com is not affiliated with any of the institutions featured in this website. It is always recommended to visit an institutions or sources official website for more information. In the same vein, all comments placed here do not represent the opinion of schoolngr.com

Register • Login