Potholes on a highway can be a serious problem and are in constant need of repair. With a particular type of terrain and make of concrete, past experience suggests that there are, on the average, 2 potholes per mile after a certain amount of usage. It is assumed that the Poisson process applies to the random variable "number of potholes" (a) What is the probability that no more that one pothole will appear in a section of one mile? (b)What is the probability that no more that 4 potholes will occur in a given section of 5 miles?

answer:

for a mean of m, the poisson formula is

P(k) = e^-m *m^k/k!

a. m = 2, P(≤1) = P(0) + P(1) = e^-2(1 +2) = .4060 <

b. m = 2*5, P(≤4)  

= e^-10(1 + 10 + 10^2/2! + 10^4/4!) = .0293 <

Step-by-step explanation:

50- 250 is correct i did that one too

step-by-step explanation:

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;