1. A study by a survey group shows that 58.7% of households have a pet dog. a. F
ID: 2982327 • Letter: 1
Question
1. A study by a survey group shows that 58.7% of households have a pet dog.
a. For a randomly selected group of 75 households, find the mean and standard deviation for the number that have a pet dog.
b. Based on this survey, would it be unusual to find that 55 households have a pet dog? (Explain your answer.)
2. For a 30 day period, there were 97 babies born in a certain hospital.
a. Find the expected number of babies born per day based on this information.
b. Find the probability that, for a randomly selected day, there were exactly 5 babies born in this hospital.
c. Find the probability that, for a randomly selected day, there was at least 1 baby born in this hospital.
Explanation / Answer
1. A study by a survey group shows that 58.7% of households have a pet dog.
a. For a randomly selected group of 75 households, find the mean and standard deviation for the number that have a pet dog.
mean = np = 75*0.587 = 44.025
s.d = sqrt(n*p*(1-p) = sqrt(75*0.587*(1-0.587) = 4.26
b. Based on this survey, would it be unusual to find that 55 households have a pet dog? (Explain your answer.)
no
it is likely that 44 can have pet dogs..not 55.
2. For a 30 day period, there were 97 babies born in a certain hospital.
a. Find the expected number of babies born per day based on this information.
expected number of babies born per day = 97/30 = 3.233 ( since this cant be fractions)
= 3
b. Find the probability that, for a randomly selected day, there were exactly 5 babies born in this hospital.
P(x=5) = e^-3 3^5/5! = e^-3 3^5/5! = 0.1008
c. Find the probability that, for a randomly selected day, there was at least 1 baby born in this hospital
P(x>=1) = 1 - P(x=0) = 1 - e^-3 3^0/0! = 0.9502
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