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What is The PEFR of a group of 11 year old girls follow a normal distribution with mean 300 1/min and standard deviation 201/min and explain in detail?
In Normal distribution,

– Mean ± 1SD (m ± 1σ) covers 68% values
– Mean ± 2SD (m ± 2σ) covers 95% values
– Mean ± 3SD (m ± 3σ) covers 99% values
In the given question,

Mean of PEFR (μ) = 300 l/min
Standard deviation of PEFR (σ) = 20 l/min

Thus,

68% of girls will have PEFR in the range Mean ± 1SD (m ± 1σ) = 300 ± 20 l/min, i.e. between (300 – 20) and (300 + 20) 1/min

– 280 – 320 l/min range covers 68% of girls

95% of girls will have PEFR in range Mean ± 2SD (m ± 2σ) = 300 ± 2(20) l/min, i.e. between (300 – 40) and (300 + 40) 1/min

– 260 – 340 l/min range covers 95% of girls

99% of girls will have PEFR in range Mean ± 3SD (m ± 3σ) = 300 ± 3(20) l/min, i.e. between (300 – 60) and (300 + 60) 1/min

– 240 – 360 l/min range covers 99% of girls

Now, 260 – 340 l/min range covers 95% of girls, thus rest 5% of girls are outside this range, i.e. they have PEFR either < 260 l/min or > 340 l/min

– Even this will be symmetrically distributed (Normal curve is bilaterally symmetrical), thus

2.5% girls will have PEFR < 260 l/min
2.5% girls will have PEFR > 340 l/min

– Girls having PEFR less than 340 l/min: 97.5%

Since the normal range of PEFR for girls is not given in the question, it cannot be concluded that all girls have healthy lungs.