1. Assume X ∼ N(20, 25), (a) find P(X > 25) (b) the value of x...

1. Assume X ∼ N(20, 25),

(a) find P(X > 25)

(b) the value of x if P(X > x) = 0.975.

(c) find the values of a and b, two symmetrical values about 20 such that P(a < X < b) = 0.95.

(d) If X1, X2, . . . , X100 is random sample for the distribution of X

• what is the sampling distribution of the sample mean X¯?

• find P(X >¯ 20.50)

(e) Suppose the proportion of voters who support Proposition A is π = 0.40. Suppose a random sample of size n = 100 is taken from this population and let p be the proportion in the sample of those who support this proposition. i. What is the sampling distribution of p? ii. Find P(0.35 < p < 0.45).

(f) Suppose X ∼ Bin(10, 0.5). Find P(X = 5).

(g) If X¯ = 25, n = 36 and σ = 12, construct a 95% confidence interval for µ

(h) Suppose in the previous question that s = 12 and the sample was taken from a normal distribution. Find a 95% confidence interval for µ.

Expert Solution

orchestra answered 2 years ago

Find test statistic and p-value and make conclusion for MEAN: x=35, n=200, Ho: p=25%, H1: p<25%,...

Find test statistic and p-value and make conclusion for MEAN: x=35, n=200, Ho: p=25%, H1: p<25%, confidence level=0.05 Then find test statistic and p-value and make conclusion for PROPORTION: x̄=37, s=10.2, n=30, Ho: μ=32, H1: μ≠32, confidence level=0.01 Now find test statistic and p-value and make conclusion for TWO PROPORTIONS: x1 = 6, n1 = 315, x2 = 80, n2 = 320, Ho: p1 = p2, HA: p1 < p2, α = 0.1

Find P VALUE and make conclusion for MEAN: x=35, n=200, Ho: p=25%, H1: p<25%, confidence level=0.05...

Find P VALUE and make conclusion for MEAN: x=35, n=200, Ho: p=25%, H1: p<25%, confidence level=0.05 Find P VALUE and make conclusion for PROPORTION: x̄=37, s=10.2, n=30, Ho: μ=32, H1: μ≠32, confidence level=0.01 Find test statistic AND P VALUE and make conclusion for TWO PROPORTIONS: x1 = 6, n1 = 315, x2 = 80, n2 = 320, Ho: p1 = p2, HA: p1 < p2, α = 0.1

9. Let X ~ N(194; 24). Find: (a) P(X <= 218) (b) P(145 < X <...

9. Let X ~ N(194; 24). Find: (a) P(X <= 218) (b) P(145 < X < 213) (c) The first quartile for X (d) The third quartile for X (e) the IQR for X (f) P(|X-194|> 41) 10. A soft drink machine discharges an average of 345 ml per cup. The amount of drink is normally distributed with standard deviation of 30 ml. What fraction of cups will contain more than 376 ml? (Keep 4 decimals)

Let X ~ N(190; 23). Find: (a) P(X <= 213) (b) P(148 < X < 202)...

Let X ~ N(190; 23). Find: (a) P(X <= 213) (b) P(148 < X < 202) (c) The first quartile for X (d) The third quartile for X (e) the IQR for X (f) P(|X-190|> 34

Let X ~ N(196; 19). Find: (a) P(X </= 223) (b) P(143 < X < 206)...

Let X ~ N(196; 19). Find: (a) P(X </= 223) (b) P(143 < X < 206) (c) P(|X-196|> 30)

Find the following probabilities. A.) P(X=5), X FOLLOWING A BINOMIAL DISTRIBUTION, WITH N=50 AND P=.7. B.)...

Find the following probabilities. A.) P(X=5), X FOLLOWING A BINOMIAL DISTRIBUTION, WITH N=50 AND P=.7. B.) P(X = 5), X following a Uniform distribution on the interval [3,7]. c.) P(X = 5), X following a Normal distribution, with µ = 3, and σ = .7. (To complete successfully this homework on Stochastic Models, you need to use one of the software tools: Excel, SPSS or Mathematica, to answer the following items, and print out your results directly from the software....

Considerapopulationwhoseprobabilitiesaregivenby p(1)=p(2)=p(3)= 1 3 (a) DetermineE[X]. (b) DetermineSD(X). σ2σ n =√n SD(X)= In the preceding formula,...

Considerapopulationwhoseprobabilitiesaregivenby p(1)=p(2)=p(3)= 1 3 (a) DetermineE[X]. (b) DetermineSD(X). σ2σ n =√n SD(X)= In the preceding formula, σ is the population standard deviation, and n is the (c) Let X denote the sample mean of a sample of size 2 from this population. Determine the possible values of X along with their probabilities. (d) Usetheresultofpart(c)tocomputeE[X]andSD(X). (e) Areyouranswersconsistent?

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1. Assume X ∼ N(20, 25), (a) find P(X > 25) (b) the value of x...

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