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lisov135 [29]
2 years ago
7

Given that x is a normal variable with mean μ = 47 and standard deviation σ = 6.3, find the following probabilities. (Round your

answers to four decimal places.) (a) P(x ≤ 60) (b) P(x ≥ 50) (c) P(50 ≤ x ≤ 60)
Mathematics
1 answer:
Amanda [17]2 years ago
7 0

Answer:

(a) P\left ( x\leq 60 \right )=0.9803, (b) P\left ( x\geq 50 \right )=0.3156, (c) P(50 \leq  x \leq 60)=0.2959

Step-by-step explanation:

Given that mean \mu =47 and standard deviation \sigma =6.3

(a) We need to find P\left ( x\leq 60 \right ). Using z score

z=\frac{x-\mu }{\sigma }=\frac{60-47}{6.3}=2.063492

So,

P\left ( x\leq 60 \right )=P\left ( z\leq 2.063492 \right )=0.9803

(b) We need to find P\left ( x\geq 50 \right ). Using z score

z=\frac{x-\mu }{\sigma }=\frac{50-47}{6.3}=0.4761904

So,

P\left ( x\geq 50 \right )=P\left ( z\geq 0.4761904 ) \right )=1-P\left ( z\leq  0.4761904 ) \right )=1-0.6844=0.3156

(c) We need to find P(50 \leq  x \leq 60). From above z scores

P(50 \leq  x \leq 60)=P\left ( 0.4761904\leq z\leq2.063492  \right )=0.2959

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