Answer:
a) No 95% of values will fall between (24;64); 68,27% will fall between (34;54)
b)71,83 % will fall between 34 and 64 ounces
Step-by-step explanation:
Empirical rule establishes, for a normal distribution with mean μ and σ as standard deviation:
In interval μ ± σ or ( μ + σ ; μ - σ) we should find 68.27 % of all values of the population, and by simmetry 68.27/2 = 34,14 % should be over the mean and the other half would be values below the mean
Therefore in our case
μ + σ = 44 + 10 = 54
And
μ - σ = 44 - 10 = 34
a) Then 68,34 % of values will fall in this interval
We know now that value 34 is 1* σ below the mean, and is at the limit of 34,14 %
b) μ + 2*σ = 44 * 2*10 = 44 + 20 = 64
64 is the upper limit for the interval μ + 2*σ and we know that 95.45 % of all values will fall between ( μ - 2*σ ; μ + 2*σ ) and by simmetry just one side of this interval (the right side ) will have 95.45/2 = 47;73 %
Then in interval going from ( 34 ; 64 ) we shoud find 47.73 + 34,14
71,83 % of all values will fall between 34 and 64
