(a)The age of patients in a hospital is normallydistributed with mean 45.8 years with a standarddeviation of 17.7 years.(i)A patient is randomly selected from the hospital.What is the probability that he/she is more than 40years?12.1% of the patients in this hospital aged morethan x years old. Find the value of x.(iii)A random sample of 30 patients was taken fromthe hospital. What is the probability that the sampleyields a mean age of less than 50 years?

Answered: Image /qna-images/answer/6345eb5a-494f-4192-bab6-c2043e9d575e.jpg

Answered: (a) The age of patients in a hospital…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Assume that the square footage of a residential house in the US is normally distributed with a mean=1000 and standard deviation=150 square feet. If we select a random house what is the probability that it will be at most 1050 square feet?
The height of American women is believed to follow a normal distribution with mean μ = 5.38 feet and standard deviation σ = 0.2083 feet. (b) A study randomly selects 30 American women. What is the probability that the mean height of women in this sample is greater than 5.5 feet? (c) Another study randomly selects 50 American women. Will there be a lower or higher probability that the mean height of the 50 women in this sample is greater than 5.5 feet, compared to the study in part (b)? Explain. (d) Instead, for which of the two studies from parts (b) and (c) there is a higher probability that the mean height of the women in the sample is between 5.33 and 5.43 feet? Explain.
Fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 42 randomly selected people who train in groups and finds that they run a mean of 47.1 miles per week. Assume that the population standard deviation for group runners is known to be 4.4 miles per week. She also interviews a random sample of 47 people who train on their own and finds that they run a mean of 48.5 miles per week. Assume that the population standard deviation for people who run by themselves is 1.8 miles per week. Test the claim at the 0.01 level of significance. Let group runners training for marathons be Population 1 and let individual runners training for marathons be Population 2. Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places.
The time taken by employees at Grace Floral shop to put a bouquet together has a normal distribution with mean 26.4 minutes and standard deviation .8 minutes. (i) Find the probability that an employee chosen at random takes between 24.6 and 27.8 minutes to put a bouquet together. (ii) 12% of employees take more than t minutes to put a bouquet together. (ii) Find the value of t.
The length of pregnancy follows a normal distribution with a mean of 268 days and a standard deviation of 15 days. What is the probability a randomly selected pregnancy is more than 265 days in length? What length of pregnancy separates the shortest and longest 10% of from the rest? Would it be unusual to select a pregnancy that lasts longer than 290 days? If so, why?
The mean ACT composite score in a recent year is 20.8 with a standard deviation of 5.6. A random sample of 36 ACT composite scores are selected. What is the probability that the mean score for the sample is less than 21.6?
Scores for men on the verbal portion of the SAT-I test are normally distributed with a mean of 509 and a standard deviation of 112(a) If 1 man is randomly selected, find the probability that his score is at least 570.(b) If 19 men are randomly selected, find the probability that their mean score is at least 570.19 randomly selected men were given a review course before taking the SAT test. If their mean score is 570, is there a strong evidence to support the claim that the course is actually effective?(Enter YES or NO)
pizza delivery chain advertises that it will deliver your pizza in 35 minutes from when the order is placed. Being a skeptic, you decide to test and see if the mean delivery time is actually more than 35 minutes. For the simple random sample of 7 customers who record the amount of time it takes for each of their pizzas to be delivered, the mean is 39.4 minutes with a standard deviation of 5.5 minutes. Assume that the population distribution is approximately normal. Perform a hypothesis test using a 0.025 level of significance. Step 3 of 3 : Draw a conclusion and interpret the decision.
The length of human pregnancies from conception to birth approximates a normal distribution with a mean of 266 days and a standard deviation of 16 days. What proportion of all pregnancies will last between 240 and 270 days. (b) 0.5471 (d) 0.6875 (a) 0.8674 (c) 0.9876 Answer:
The mean ACT composite score in a recent year is 20.8 with a standard deviation of 5.6. A random sample of 36 ACT composite scores are selected. What is the probability that the mean score for the sample is (b) more than 19.8
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7. The heights of women follow a normal distribution with a mean of 64.5 inches and a standard deviation of 2.8 inches. (a) (2 points) What percent of women are taller than 72 inches (6 feet)? (b) (4 points) From a SRS of 50 women, what is the probability that their mean height is between 60 inches and 72 inches?

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