Question

1. The song-length of tunes in the Big Hair playlist of a certain Statistics professors mp3-player vary from song to song. This variation can be modeled by the Normal distribution, with a mean song-length of μ=4.1 minutes and a standard deviation of σ=0.7 minutes. Note that a song that has a length of 4.5 minutes is a song that lasts for 4 minutes and 30 seconds.

From the time he set his mp3-player to shuffle, there has been 16 songs randomly chosen and played in succession. What is the chance that the 16-th song played is the 8-th to be longer than 4.1 minutes? Enter your answer to four decimals.

2. The number of people arriving per hour at the emergency room (ER) of a local hospital seeking medical attention can be modeled by the Poisson distribution, with a mean of 10 people per hour.

The inter-arrival time, X X, is defined as the time that passes between successive arrivals of patients seeking medical attention. It has been 5 minutes since the last person seeking medical attention arrived at the ER. What is the probability that at least 11 minutes (in total) will pass until the next medical-attention-seeking person passes through the ER doors? Use four decimals in your answer.

3.The number of customers entering a 24-hour convenience store every 10-minutes can be modeled by the Poisson distribution with a a mean of λ=5.2 customers. You are to look at the amount of time passing between successive customers entering the convenience store, represented by X

Compute the probability at most 3 minutes will pass between the arrival of one customer and the next customer. In answering this question, be sure to use your answer in (a) to two decimals. Enter your answer using four decimals

At least 1 minute has passed since the last customer entered the store. What is the probability that in total, at least 4 minutes will pass until the next customer enters this store? Use four decimals in your answer.

Answer 1