8. The lengths of rods from a certain factory are normally distributed with mean uem and standard deviation 6cm. It is known that 4.78% of the rods have lengths greater than 82em. Find to the nearest integer. (i). the mean u. (ii) the range, a (symmetrical about the mean) within which 75% of the lengths of the rods lie. F'ind also, to 4 decimal places

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Answer i, ii, iii,

8. The lengths of rods from a certain factory are normally distributed with mean ucm and standard
deviation 6cm. It is known that 4.78% of the rods have lengths greater than 82cm.
Find to the nearest integer,
(i). the mean 4.
(ii) the range, a (symmetrical about the mean) within which 75% of the lengths of the rods lie.
l'ind also, to 4 decimal places,
(ii) the probability that a rod chosen at random has a length between 62em and 72cm.
Transcribed Image Text:8. The lengths of rods from a certain factory are normally distributed with mean ucm and standard deviation 6cm. It is known that 4.78% of the rods have lengths greater than 82cm. Find to the nearest integer, (i). the mean 4. (ii) the range, a (symmetrical about the mean) within which 75% of the lengths of the rods lie. l'ind also, to 4 decimal places, (ii) the probability that a rod chosen at random has a length between 62em and 72cm.
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