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'?