Question

(c) The number of cars arriving at a toll booth follows a Poisson distribution with a mean of 3 cars per five-minutes. What is the probability of 3 cars arriving over a five-minute interval? 5. (a) The average waiting time that people spend going through airport security for planes at an airport is 21 minutes with a standard deviation of 4.2 minutes. (i) What is the probability that the average waiting time for 40 people is more than 22 minutes? (ii) The probability that 100 randomly chosen people have an average waiting time less than a certain average time is 0.1788. What is the average time? (b) Suppose that X1, ..., X25 is a random sample from a normal population N(?, ?²) and that the sample mean x? = 148.30. (i) If ? = 4, find a 95% confidence interval for ?. (ii) If the sample standard deviation s = 3 and ? is unknown, find a 90% confidence interval for ?.

          (c) The number of cars arriving at a toll booth follows a Poisson distribution with a mean of 3 cars per five-minutes. What is the probability of 3 cars arriving over a five-minute interval?
5. (a) The average waiting time that people spend going through airport security for planes at an airport is 21 minutes with a standard deviation of 4.2 minutes.
(i) What is the probability that the average waiting time for 40 people is more than 22 minutes?
(ii) The probability that 100 randomly chosen people have an average waiting time less than a certain average time is 0.1788. What is the average time?
(b) Suppose that X1, ..., X25 is a random sample from a normal population N(?, ?²) and that the sample mean x? = 148.30.
(i) If ? = 4, find a 95% confidence interval for ?.
(ii) If the sample standard deviation s = 3 and ? is unknown, find a 90% confidence interval for ?.

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(c) The number of cars arriving at a toll booth follows a Poisson distribution with a mean of 3 cars per five-minutes. What is the probability of 3 cars arriving over a five-minute interval?
5. (a) The average waiting time that people spend going through airport security for planes at an airport is 21 minutes with a standard deviation of 4.2 minutes.
(i) What is the probability that the average waiting time for 40 people is more than 22 minutes?
(ii) The probability that 100 randomly chosen people have an average waiting time less than a certain average time is 0.1788. What is the average time?
(b) Suppose that X1, ..., X25 is a random sample from a normal population N(?, ?²) and that the sample mean x? = 148.30.
(i) If ? = 4, find a 95% confidence interval for ?.
(ii) If the sample standard deviation s = 3 and ? is unknown, find a 90% confidence interval for ?.

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Madhur L

07/25/2023

Step 1

We want to find the probability of 3 cars arriving over a five-minute interval. The Poisson distribution formula is: P(X = k) = (e^(-λ) * λ^k) / k! where λ is the mean and k is the number of events. In this case, λ = 3 (since the mean is 3 cars per Show more…

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(c) The number of cars arriving at a toll booth follows a Poisson distribution with a mean of 3 cars per five-minutes. What is the probability of 3 cars arriving over a five-minute interval? 5. (a) The average waiting time that people spend going through airport security for planes at an airport is 21 minutes with a standard deviation of 4.2 minutes. (i) What is the probability that the average waiting time for 40 people is more than 22 minutes? (ii) The probability that 100 randomly chosen people have an average waiting time less than a certain average time is 0.1788. What is the average time? (b) Suppose that X1, ..., X25 is a random sample from a normal population N(μ, σ²) and that the sample mean x̄ = 148.30. (i) If σ = 4, find a 95% confidence interval for μ. (ii) If the sample standard deviation s = 3 and σ is unknown, find a 90% confidence interval for μ.

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Transcript

00:01 Hello students in this question x follows poisson distribution with lambda equal to 3.

00:05 So we have the pmf of poisson distribution as probability of x equal to x e power minus lambda lambda power x divided by x factorial where x takes value 0 1 so on.

00:18 So here we need to find probability of x equals to 3 that means e power minus 3 e power 3 divided by 3 factorial and that is equal to 0 .2 2 4 0 and for the next question let x be the random variable that the waiting time that people that people spend going through airport security airport security for planes at an airport.

01:09 So here x has mean 21 minutes and the standard deviation 4 .2 minutes.

01:20 So here we need to find probability of x bar is greater than 22.

01:24 So here we have n is equal to 40 the probability of x bar minus mu divided by sigma divided by root n is greater than 22 minus 21 divided by sigma by root n is 0 .66.

01:45 So this can be written as probability of z is greater than 1 .51 that is 1 minus probability of z is less than 1 .51.

01:55 So from the standard normal table 1 minus 0 .9 3 3 9 so that is equal to 0 .066 1 and for the next question here we have n equal to 100.

02:13 So here probability of x bar less than x is equal to 0 .1788.

02:19 So this is a standard normal curve and here this is mean.

02:27 So here this value this is 0 .1788.

02:33 So here we can calculate the value we have z is equal to x bar minus mu divided by sigma divided by root n.

02:43 So here from the standard normal table the value of z is minus 0 .92.

02:52 So z into sigma divided by root n is equal to x bar minus mu.

02:59 So x bar is equal to mu plus z sigma divided by root n.

03:04 So now substituting the values x bar is equal to 21 plus minus 0 .92 into 42 divided by root 100...

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