Answer to Question #220491 in Statistics and Probability for Vickie

Question #220491
a sample of 600 respondents the monthly income of the respondents follow a normal distribution with its mean and standard deviation at 30,000 and 6000 respectively
What is the probability that monthly income is between 20000 and 34000
Probability that a monthly income is more than 32,000
How many people Expected to have the income between 20,000 and 34000
What is the probability that the monthly income is less than 24,000
1
Expert's answer
2021-07-26T14:27:20-0400

N=600μ=30000σ=6000N=600 \\ \mu=30000 \\ \sigma = 6000

Is it justifiable to exclude homemakers’ value creation from national income?

P(20000<X<34000)=P(X<34000)P(X<20000)=P(Z<34000300006000P(Z<20000300006000)=P(Z<0.666)P(Z<1.666)=0.74760.0478=0.6998P(20000<X<34000) = P(X<34000) -P(X<20000) \\ = P(Z< \frac{34000-30000}{6000} -P(Z< \frac{20000-30000}{6000}) \\ =P(Z< 0.666) -P(Z< -1.666) \\ = 0.7476 -0.0478 \\ = 0.6998

Probability that a monthly income is more than 32,000

P(X>32000)=1P(X<32000)=1P(Z<32000300006000)=1P(Z<0.3333)=106304=0.3696P(X>32000) = 1 -P(X<32000) \\ = 1 -P(Z< \frac{32000-30000}{6000}) \\ = 1 -P(Z< 0.3333) \\ = 1 -06304 \\ = 0.3696

How many people Expected to have the income between 20,000 and 34000

Number of people =N×P(20000<X<34000)= N \times P(20000<X<34000)

=600×0.6998=419.88420= 600 \times 0.6998 \\ = 419.88 ≈420

What is the probability that the monthly income is less than 24,000

P(X<24000)=P(Z<24000300006000)=P(Z<1)=0.1586P(X< 24000) = P(Z< \frac{24000-30000}{6000}) \\ = P(Z< -1) \\ = 0.1586


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Comments

Vickie
26.07.21, 21:49

Thank u

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