'X' is a continuous random variable which is normally distributed with 485 as the mean and 23 as the standard deviation. What percentage of Items will be found between 450 and 485.
Answers
Answer:
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Explanation:
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Answer:
The answer is 7%.
Explanation:
i) In a continuous random variable, if the data is normally distributed, it means the data is spread symmetrically around the mean.
ii) According to the three sigma rule, following is the distribution of data in normal distribution:
(Mean = x, Standard deviation = σ)
From x to x+σ: 34%
From x to x-σ: 34%
From x+σ to x+2σ: 13.5%
From x-σ to x-2σ: 13.5%
From x+2σ to x+3σ: 2.5%
From x-2σ to x-3σ: 2.5%
iii) Given,
Mean = x = 485
Standard deviation = σ = 23
iv) 450 is 485 - 35 i.e. x-1.5σ.
Hence, the range of 450-485 will contain approximately half the percentage of items in x-σ to x-2σ i.e. 13.5%.
v) Hence, approx. 7% of the items will be found between 450 and 485.
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