The amount of syrup that people put on their pancakes is normally distributed with mean 55 mL and standard deviation 10 mL. Suppose that 47 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible.

(a) What is the distribution of X? X ~ N(,)(b) What is the distribution of x̄? x̄ ~ N(,)(c) If a single randomly selected individual is observed, find the probability that the amount of syrup this person consumes is between…

Jim’s systolic blood pressure is a random variable with a mean of 143 mmHg and a standard deviation of 15 mmHg. For Jim’s age group, 140 is the threshold for high blood pressure.(a) If Jim’s systolic blood pressure is taken at a randomly chosen moment, what is the probability that it will be 137 or less?(b) If Jim’s systolic blood pressure is taken at a randomly chosen moment, what is the probability that it will be 178 or more?

Answer : Given information : The population mean (μ)=143 The population standard deviation (σ)=15 Solution : A) The probability that it will be 137 or less : $$P(x \leq 137) = P\left(\frac{x – \mu}{\sigma} \leq \frac{137…