Question

Suppose that 73% of Santa Ana residents are Latino. You select a sample of 18 residents? please use appropriate notation for each queation. for example: P(X=13) please also calculate your answers with 4 decimal places.

A) what is the probability that exactly 13 of the residents are Latino?

B) what is the probability that at most 15 residents are Latino?

C) what is the probability that between 10 and 16 residents are Latino?

D) what is the mean number of Latinos for a distribution of 18 residents. show your work no probability notation needed.

E) what is the standard deviation of Latinos for the distribution of 18 residents. show your work no probability notation needed?

F) using the mean and standard deviation from D and E is a sample of 18 with only nine Latinos considered unusual?

Compute without using combinations. please be neat and show all your work.

Answer 1

The distribution of the number of Latinos out of 18 residents here is modelled as:

a) The probability that exactly 13 of the residents are Latino is computed using the Binomial probability function here as:

Therefore 0.2055 is the required probability here.

b) The probability that at most 15 residents are Latino is computed here as:
P(X <= 15) = 1 - P(X = 16) - P(X = 17) - P(X = 18)

Therefore 0.9009 is the required probability here.

c) The probability that between 10 and 16 residents are Latino is computed here as:

Therefore 0.8163 is the required probability here.

d) The mean number of residents who are latinos is computed here as:
Mean = np = 18*0.73 = 13.14

Therefore 13.14 is the required mean number of latinos here.

e) The standard deviation here is computed as:

Therefore 1.8836 is the required standard deviation here.

f) Mean - 2*Std Dev = 13.14 - 2*1.8836 = 9.37 > 9

Therefore yes 9 latinos is an unusually lower value here.