The approximate percentage of daily phone calls numbering between 36 and 56 by the receptionists is 95.44%.
In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 46 and a standard deviation of 5.
Hence, Mean,μ=46 and Standard deviation,σ=5.
To find the probability of daily phone calls numbering between 36 and 56,
P(36≤X≤56)
To convert the X score to Z score, use the formula, Z=(X-μ)/σ
Then we get,
P((36-46)/5 ≤ Z ≤ (56-46)/5) = P(-2 ≤ Z ≤ 2)
By using the property of the normal bell curve, we get
P(-2 ≤ Z ≤ 2) = P(2 ≤ Z) - P(-2 ≤ Z)
As per the normal distribution table,
P(2 ≤ Z) - P(-2 ≤ Z) = 0.9772-0.0228
∴ P(36≤X≤56) = 0.9544
Hence, the approximate percentage of daily phone calls numbering between 36 and 56 by the receptionists is 95.44%.
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