Question

3. Suppose you are interested in determi Let X - weight (pounds) of a randomly selected Cavalier King ds and population you know that X is normally population mean standard deviation ơ 0.8 pounds. ning the mean weight of Cavalier King Charles Spaniel dogs. y distributed with population mean μ = 16.5 pounds and population a. Completely specify the sampling distribution for a sample size of 4, i.e. show XN(H, ) What percentage of groups of 4 Cavalier King Charles Spaniels will have an average weight between 14.5 and 17 pounds? b. As a peony enthusiast, you want to know how long the average flower bud stays in bloom. Let X length of time that a peony bloom lasts. Due to your prior research, you know that the population standard deviation ơ-2.5 days and that the lifespan is approximately normally distributed. From a sample of 9 peonies, you calculated the sample mean bloom length 17 days. 4. c. Find and interpret a 90% confidence interval for the true mean lifespan of a peony bloom. d. What samp le size would be needed for a 90% confidence interval to have a margin of error of no more than 1 day?

Answer 1

3. Here it is given that population is normally distributed with mean=16.5 and standard deviation=0.8

a. As per central limit theorem, distribution of sample mean is also normal with mean=16.5 and standard deviation=0.8/sqrt(n)=0.8/2=0.4

Hence

T~ V(16.5.0.4)

b. Now we need to find

P(14.5 T< 17)

As from a sample mean is normally distributed we can convert it to z

17 - 16.5 0.4 P(14.5 < T < 17) = P( 1.25) = 0.8943 0.4

Hence 89.43% of groups of 4 lies between 14.5 to 17