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.

(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.

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orchestra answered 1 year ago

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