The weights of a large number of miniature poodles are approximately normally distributed with a mean of 9 kilograms and a standard deviation of 0.9 kilogram. If measurements are recorded to the nearest tenth of a kilogram, find the proportion of these poodles with weights:

(a) over 10.3 kilograms; (b) of at most 9.5 kilograms; (c) between 8.3 and 10.4 kilograms inclusive. Answer : Given : The population mean $(μ) = 9$ The population standard deviation $(σ) = 0.9$ Solution : a) The probability that…

Suppose the average price of gasoline for a city in the United States follows a continuous uniform distribution with a lower bound of 3.10 per gallon and an upper bound of 3.70 per gallon. What is the probability a randomly chosen gas station charges more than 3.25 per gallon?

Answer : Given : The lower bound, $a=3.10$ The upper bound, $b=3.70$ Solution : → The probability that a randomly chosen gas station charges more than $3.25 per gallon : $$\therefore P(x > 3.25) = \int_{3.25}^{3.7} f(x) \, dx$$ $$=…

A simple random sample of size n=12

is obtained from a population with μ=64 and σ=14. (a) What must be true regarding the distribution of the population to use the normal model to compute probabilities involving the sample mean? Assuming that this condition is true, describe the sampling distribution…

Given a normal distribution with

Given a normal distribution with μ=50 and σ=3, complete parts (a) through (d). A) What is the probability that x>45 ? B) What is the probability that x<44 ? C) For this distribution, 9% of the values are less than what x-value? D) Between what two x-values (symmetrically distributed around the mean) are 60% of the values? Answer: Given Data…