QUESTION 5A study was conducted to determine the duration of a typical consultation in an urban medical practice. The results showed that the length of a consultation could be closely approximated by a normal distribution with a mean of 12.4 minutes and a variance of 9.75 minutes2.a) Find the probability that a consultation would last less than 9 minutes. (3 decimal places)b) How many of the individual patients visiting the medical centre will have a consultation time of less than 9 minutes if there are 522 individual patient consultations on a given day? Use your rounded answer, with 3 decimal places, from part a. (Round your answer to the nearest whole number)
Question
QUESTION 5A study was conducted to determine the duration of a typical consultation in an urban medical practice. The results showed that the length of a consultation could be closely approximated by a normal distribution with a mean of 12.4 minutes and a variance of 9.75 minutes2.a) Find the probability that a consultation would last less than 9 minutes. (3 decimal places)b) How many of the individual patients visiting the medical centre will have a consultation time of less than 9 minutes if there are 522 individual patient consultations on a given day? Use your rounded answer, with 3 decimal places, from part a. (Round your answer to the nearest whole number)
Solution
a) To find the probability that a consultation would last less than 9 minutes, we first need to standardize the value 9 using the z-score formula:
Z = (X - μ) / σ
where X is the value we are interested in (9 in this case), μ is the mean (12.4), and σ is the standard deviation. The standard deviation is the square root of the variance, so in this case, it is √9.75 = 3.12 (rounded to two decimal places).
Z = (9 - 12.4) / 3.12 = -1.09 (rounded to two decimal places)
We then look up this z-score in a standard normal distribution table or use a calculator with a normal distribution function to find the probability. The probability that Z is less than -1.09 is 0.138 or 13.8%.
b) If there are 522 individual patient consultations on a given day, and each consultation has a 13.8% chance of lasting less than 9 minutes, then we would expect approximately 0.138 * 522 = 72.03 of these consultations to last less than 9 minutes. Rounding to the nearest whole number, we would expect approximately 72 consultations to last less than 9 minutes.
Similar Questions
The manager of a computer shop is recording the time taken for customers to decide of which computer and accessories they buy from the time they enter the store. From the previous data, it is known that the average ‘decision’ time was 45 minutes. The manager assumes a normally distributed population with a standard deviation of 10 minutesa) What is the probability that a customer will take more than 60 minutes?b) What proportion of customers will take between 35 and 60 minutes?c) From a sample of 36 customers, what is the probability that the sample mean will be less than 40 minutes?d) Is the sample taken in c) assumed to be normally distributed? Why? What theorem is used to support this assumption?
The length of time for long-distance phone calls has been found to be normally distributed, with a mean of 20.8 minutes and a standard deviation of 6.7 minutes. In a randomly selected sample of 68 calls, what is the sample average call time below which 10% of sample average call times will be shorter? (2 decimal places)
The time to resolve a problem at a technical helpdesk in a mobile phone company is normally distributed with a mean of 17 minutes and a standard deviation of 3 minutes. a) For a randomly selected customer, find the probability that his problem can be solved in less than 12 min. b) For a randomly selected customer, find the probability that his problem can be solved between 18 mins and 20 mins. c) 40% of the customers are dissatisfied with the waiting time. What is the minimum waiting time for a dissatisfied customer?
Question 7A statistical analysis of 2,000 long-distance telephone calls made from the headquarters of theBricks and Clicks Computer Corporation indicates that the length of these calls is normallydistributed, with 𝜇 = 300 seconds and 𝜎 = 50 seconds. (4 marks)(a) What is the probability that a call lasted less than 210 seconds?(b) What is the probability that a call lasted between 210 and 320 seconds?(c) What is the probability that a call lasted between 100 and 210 seconds?(d) 10% of all calls will last less than how many seconds?
Suppose the commute times for employees of a large company follow a normal distribution. If the mean time is 22 minutes and the standard deviation is 5 minutes, 95% of the employees will have a travel time within which range?A.17.25 minutes to 26.75 minutesB.17 minutes to 27 minutesC.12 minutes to 32 minutesD.7 minutes to 37 minutesSUBMITarrow_backPREVIOUS
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.