Your department uses 5/8 boxes of envelopes each month.
2 answers:
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Answer:
(a) The value of P (X < 21 | <em>μ </em> = 23 and <em>σ</em> = 3) is 0.2514.
(b) The value of P (X ≥ 66 | <em>μ </em> = 50 and <em>σ</em> = 9) is 0.0427.
(c) The value of P (X > 47 | <em>μ </em> = 50 and <em>σ</em> = 5) is 0.7258.
(d) The value of P (17 < X < 24 | <em>μ </em> = 21 and <em>σ</em> = 3) is 0.7495.
(e) The value of P (X ≥ 95 | <em>μ </em> = 80 and <em>σ</em> = 1.82) is 0.
Step-by-step explanation:
The random variable <em>X</em> is Normally distributed.
(a)
The mean and standard deviation are:
Compute the value of P (X < 21) as follows:
Thus, the value of P (X < 21 | <em>μ </em> = 23 and <em>σ</em> = 3) is 0.2514.
(b)
The mean and standard deviation are:
Compute the value of P (X ≥ 66) as follows:
Use continuity correction.
P (X ≥ 66) = P (X > 66 - 0.5)
= P (X > 65.5)
Thus, the value of P (X ≥ 66 | <em>μ </em> = 50 and <em>σ</em> = 9) is 0.0427.
(c)
The mean and standard deviation are:
Compute the value of P (X > 47) as follows:
Thus, the value of P (X > 47 | <em>μ </em> = 50 and <em>σ</em> = 5) is 0.7258.
(d)
The mean and standard deviation are:
Compute the value of P (17 < X < 24) as follows:
Thus, the value of P (17 < X < 24 | <em>μ </em> = 21 and <em>σ</em> = 3) is 0.7495.
(e)
The mean and standard deviation are:
Compute the value of P (X ≥ 95) as follows:
Use continuity correction:
P (X ≥ 95) = P (X > 95 - 0.5)
= P (X > 94.5)
Thus, the value of P (X ≥ 95 | <em>μ </em> = 80 and <em>σ</em> = 1.82) is 0.
