Question

Relax! A recent survey asked 1678 people how many hours per day they were able to relax. The results are presented in the following table. Number of Hours Frequency 0 ch . 1 2 3 4 $ 116 187 336 250 316 ille 147 6 7 8 60 1673 oce Consider these 1678 people to be a population. Let X be the number of hours of relaxation for a person sampled at random from this population Part 1 of 5 (a) Construct the probability distribution of X. Round the answer to three decimal places 0 1 2 3 4 $ 7 3 PC) Part 2 of 5 (b) Find the probability that a person relaxes more than 6 hours per day The probability that a person relaxes more than 6 hours per day is Round the answer to three decimal places.) Part 3 of 5 (c) Find the probability that a person doesn't relaxal The probability that a person doesn't relaxat al is three decimal places) Round the answer to Part 4 of 5 (d) Compute the mean, Round the answer to two decal places Part 5 of 5 (e) Compute the standard deviation Round the answer to three decimal places

Answer 1

To answer the student's question, we construct a probability distribution for the number of relaxation hours, calculate probabilities for specific conditions, and compute the mean and standard deviation. This requires the frequencies for each number of hours of relaxation.

Step-by-step explanation:

To construct the probability distribution of X, which represents the number of hours of relaxation for a person sampled at random from this population of 1678 people, we will divide the frequency of each number of relaxation hours by the total number of people surveyed. Next, we will calculate the requested probabilities and statistics based on this distribution.

• The probability P(X = x) is found by dividing the frequency of each category by the total number of responses.
• To find the probability that a person relaxes more than 6 hours per day, we add up the probabilities of X being 7 and 8 hours.
• The probability that a person doesn't relax at all is simply P(X = 0).
• For the mean, we sum the products of each number of hours and its respective probability.
• The standard deviation is computed by taking the square root of the variance, which involves summing the squared difference between each number of hours and the mean, multiplied by its probability.

We would need the actual frequencies for each number of hours of relaxation to perform the calculations and round the answers to the specified decimal places.