Question

In: Statistics and Probability

3. Assume that the time elapsed between customers entering a retail shop is exponentially decreasing by...

3. Assume that the time elapsed between customers entering a retail shop is exponentially decreasing by 15%. How long will the average customer continue to come before the shop runs out of business.

4. .The weight of the fabled Cobrafish is normally distributed with a mean of 45 kg. and a standard deviation of 6 kg. Approximately what percentage of Cobrafish (rounded to two decimal places) weigh between 30 kg. and 49 kg? Note: You must find the corresponding z-scores by hand, showing your work

5. A radar unit is used to measure speeds of cars on a motorway. The speeds are normally distributed with a mean of 90 km/hr and a standard deviation of 10 km/hr. What is the probability that a car picked at random is travelling less than 105 km/hr. Write your answer as a percentage.

Expert Solution

3.time elapsed between customers entering a retail shop is exponentially decreasing by 15%.

= 15% = 0.15

mean =

mean = 6.667

4.

The following information has been provided:

We need to compute The corresponding z-values needed to be computed are:

Therefore, we get:

5.

The following information has been provided:

We need to compute The corresponding z-value needed to be computed:

Therefore,

orchestra answered 2 years ago

" time headway" in traffic flow is the elapsed time between the time that one car...

" time headway" in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point. Let X=the time headway for two randomly chosen consecutive cars on a freeway during a period of heavy flow. Suppose that in a different traffic environment, the distribution of time headway has the form f(x)={k/x^5, x>=2 {0, x<2. a) Determine the value of k for which f(x)...

"Time headway" in traffic flow is the elapsed time between the time that one car finishes...

"Time headway" in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point. Let X = the time headway for two randomly chosen consecutive cars on a freeway during a period of heavy flow (sec). Suppose that in a particular traffic environment, the distribution of time headway has the following form. f(x) = k x7 x > 1 0 x...

Suppose the response time X at a certain on-line computer terminal (the elapsed time between the...

Suppose the response time X at a certain on-line computer terminal (the elapsed time between the end of a user's inquiry and the beginning of the system's response to that inquiry) has an exponential distribution with expected response time equal to 5 seconds. a) Find E(X) b) What is lamda? c) Find P(5<=X<=10) d) Find the 60th %tile.

Based on a study, the average elapsed time between when a user navigates to a website...

Based on a study, the average elapsed time between when a user navigates to a website on a mobile device until its main content is available was 14.6 seconds. This is more than a 20% increase from the previous year. Responsiveness is certainly an important feature of any website and is perhaps even more important on a mobile device. What other web design factors need to be considered for a mobile device to make it more user friendly? Among other...

Sales delay is the elapsed time between the manufacture of a product and its sale. According...

Sales delay is the elapsed time between the manufacture of a product and its sale. According an article it is quite common for investigators to model sales delay using a lognormal distribution. For a particular product, the cited article proposes this distribution with parameter values μ = 2.01 and σ2 = 0.06 (here the unit for delay is months). (a) What are the variance and standard deviation of delay time? (Round your answers to two decimal places.) variance months2 standard...

the time between phone calls received by a telephonist is exponentially distributed with a mean of...

the time between phone calls received by a telephonist is exponentially distributed with a mean of 10 minutes.what is the probability that there are no more than four calls within one hour?

mobile App Website Design. Based on a 2018 study, the average elapsed time between when a...

mobile App Website Design. Based on a 2018 study, the average elapsed time between when a user navigates to a website on a mobile device until its main content is available was 14.6 seconds. This is more than a 20% increase from 2017. Responsiveness is certainly an important feature of any website and is perhaps even more import-ant on a mobile device. What other web design factors need to be considered for a mobile device to make it more user...

The mean time between arrivals of customers in a bank is 3 minutes. Write the expression...

The mean time between arrivals of customers in a bank is 3 minutes. Write the expression for the exponential distribution for average time between arrivals for any time t (t>=0). If a customer has already arrived in the bank, what is the probability that the next customer will come after 10 minutes? What is the probability that 5 customers will arrive in the one hour interval? Answer with full steps. Thank you!, Any half answer or incomplete answer would be...

A barber shop has an average of 12 customers between 8.00am and 9.00am every Saturday. Customers arrive according to Poisson distribution. Let X represent the time between arrivals.

A barber shop has an average of 12 customers between 8.00am and 9.00am every Saturday. Customers arrive according to Poisson distribution. Let X represent the time between arrivals. (a) Construct the distribution for the random variable X? (b) Find the mean and standard deviation of X. (c) What is the probability that the time between consecutive arrivals (customers) will fall between 3 and 6 minutes?

The time T between requests to a web server is exponentially distributed with mean 0.5 seconds....

The time T between requests to a web server is exponentially distributed with mean 0.5 seconds. (a) What is the value of the parameter in this exponential distribution? Give the p.d.f. and c.d.f. of T? [2] (b) Use the c.d.f. of T to find the median request time and interpret it. [3] (c) What is the probability that the request time is between 0.25 and 1.5 seconds? [1]( d) Find the 60th percentile of the request time and interpret it....