Selasphours sasin is the scientific name for what is commonlycalled \"Allen\'s h
ID: 2913530 • Letter: S
Question
Selasphours sasin is the scientific name for what is commonlycalled "Allen's hummingbird." This beautiful hummingbird lives onthe West Coast of the United States and is named for C. A. Allen(1841-1930), who studied these birds extensively. Let x be a randomvariable that represents the incubation time for Allen hummingbirdeggs. Based on information from The Hummingbird Book, by Donald andLillian Stokes (Little, Brown, and Copany), the x distrubution hasa mean of = 16 days. Let us assume that the standarddeviation is appx = 2 days. The distrbution of x values ismore or less mound shaped and symmetrical but not necessarilynormal. Suppose that we hav n = 30 eggs in an incubator. Let _ bethe average incuation for theseeggs. x a. what can we say about the probability distrubution of _? Isit appx normal? What are the mean and standarddeviation? x b. What is the probability that _ is between 16 and 17days? x c. What is the probability that _ is less than 15 days? x Selasphours sasin is the scientific name for what is commonlycalled "Allen's hummingbird." This beautiful hummingbird lives onthe West Coast of the United States and is named for C. A. Allen(1841-1930), who studied these birds extensively. Let x be a randomvariable that represents the incubation time for Allen hummingbirdeggs. Based on information from The Hummingbird Book, by Donald andLillian Stokes (Little, Brown, and Copany), the x distrubution hasa mean of = 16 days. Let us assume that the standarddeviation is appx = 2 days. The distrbution of x values ismore or less mound shaped and symmetrical but not necessarilynormal. Suppose that we hav n = 30 eggs in an incubator. Let _ bethe average incuation for theseeggs. x a. what can we say about the probability distrubution of _? Isit appx normal? What are the mean and standarddeviation? x b. What is the probability that _ is between 16 and 17days? x c. What is the probability that _ is less than 15 days? xExplanation / Answer
Let x be arandom variable for incubation time for hummingbird eggs. The xdistribution has mean of = 16 days. Let us assume that thestandard deviation is appox = 2 days. The distribution of xvalues is more or less mound shaped and symmetrical but notnecessarily normal. Suppose that we have n = 30 eggs in anincubator. Let (X_bar) be the average incubation time for theseeggs.a. What canwe say about the probability distribution of (X_bar)? Is it appoxnormal? What are the mean and standarddeviation?
{Sample size N = 30 is large enoughthat probability distribution
of X_bar is approxNormal.}
{Mean Of X_bar} = = 16
{Standard Deviation OfX_bar} = s = /Sqrt[N] = (2)/Sqrt[30] = 0.3651
{Normal Z Distribution} ----> Z = ((X_bar) - )/s = ((X_bar) - (16))/(0.3651)
b. What isthe probability that (X_bar) is between 16 and 17days?
= Prob{((16) - (16))/(0.3651) < Z < ((17) - (16))/(0.3651)}
= Prob{(0) < Z < (2.739)}
= 0.4969
c. What isthe probability that (X_bar) is less than 15days? = Prob{Z < ((15)- (16))/(0.3651)}
= Prob{Z < (-2.739)}
= 0.0031