P(x < 21 | μ = 23 and σ = 3) enter the probability of fewer than 21 outcomes if the mean is 23 and the standard deviation is 3 (b) P(x ≥ 66 | μ = 50 and σ = 9) enter the probability of 66 or more outcomes if the mean is 50 and the standard deviation is 9 (c) P(x > 47 | μ = 50 and σ = 5) enter the probability of more than 47 outcomes if the mean is 50 and the standard deviation is 5 (d) P(17 < x < 24 | μ = 21 and σ = 3) enter the probability of more than 17 and fewer than 24 outcomes if the mean is 21 and the standard deviation is 3 (e) P(x ≥ 95 | μ = 80 and σ = 1.82) enter the probability of 95 or more outcomes if the mean is 80 and the standard deviation is 1.82

(a) The value of P (X < 21 | μ = 23 and σ = 3) is 0.2514.

(b) The value of P (X ≥ 66 | μ = 50 and σ = 9) is 0.0427.

(c) The value of P (X > 47 | μ = 50 and σ = 5) is 0.7258.

(d) The value of P (17 < X < 24 | μ = 21 and σ = 3) is 0.7495.

(e) The value of P (X ≥ 95 | μ = 80 and σ = 1.82) is 0.

Step-by-step explanation:

The random variable X 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 | μ = 23 and σ = 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 | μ = 50 and σ = 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 | μ = 50 and σ = 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 | μ = 21 and σ = 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 | μ = 80 and σ = 1.82) is 0.

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step-by-step explanation: