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The value of P(95 < X < 115.7) is 0.12294 and value of P(95 < M < 115.7) is 0.98.
It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.
We have:
u = 106, σ = 66.9
P(95 < X < 115.7) = P(X < 115.7) - P(X < 95)
Z(X = 115.7) = (x - μ)/σ
= (115.7 - 106)/ 66.9
= 0.14499
P(X < 115.7) = 0.55764
Similarly,
P(X < 95) = 0.4347
P(95 < X < 115.7) = 0.55764 - 0.4347
P(95 < X < 115.7) = 0.12294
For P(95 < M < 115.7) = P(M < 115.7) - P(M < 95)
Using the formula:
[tex]\rm Z = \dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
Z(M = 115.7) = 2.208460
Z(M = 95) = -2.504439
P(95 < M < 115.7) = 0.98639 - 0.0061323 = 0.98
Thus, the value of P(95 < X < 115.7) is 0.12294 and value of P(95 < M < 115.7) is 0.98.
Learn more about the normal distribution here:
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