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Sampling distribution of the sample

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Can someone please help me understand and answer the following statistical questions:

1. Suppose the random variable X is normally distributed with µ = 90 and σ2 = 16. What is the value of b such that P(X ≤ b) = 0.0062?

2. Suppose the random variable X is normally distributed with µ = 100 and σ2 = 25. What is P(100 ≤ X ≤ 115)?

3. Suppose the random variable X is normally distributed with µ = 10 and σ2 = 9. If the sample size is equal to 10, what is the sampling distribution of the sample mean, ¯ X?

4. Suppose the random variable X is normally distributed with µ = 100 and σ2 = 16. What is P( ¯ X ≥ 98) if the sample size n is equal to 4?

5. Suppose the population proportion is 0.60. If the sample size is equal to 20, what is the sampling distribution of the sample proportion, 'p-hat'?

Reference no: EM131210907

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