Suppose the mean operating time of surgeries at a hospital follows N(200, 40) in minutes. Choose an SRS of 49 people. a) What is the probability that the sample distribution x-bar takes values less than 190 minutes? Z= x = 190, μ = 200, o = 40, n = 49 x-μ O √n = 0.0401 z = -1.75, p = b) What is the probability that the sample distribution x-bar takes values greater than 205 minutes? Same formula as above, x = 205 z = 0.88, p = 0.8106 but "greater" so 1-0.8106 = 0.1894 c) What is the probability that the sample distribution x-bar takes values between 190 and 205 minutes? Between, subtract p-values, 0.8106 -0.0401 = 0.7705 d) What is the level L such that the probability of the mean operating times of surgeries greater than L is only 0.13? Greater than p = 0.13, so 1-0.13 = .87 FIND THE CLOSEST Z, z = 1.13 x = μ+Z = (200) + (1.13)) = 206.46 ***note: use sampling distribution***
Suppose the mean operating time of surgeries at a hospital follows N(200, 40) in minutes. Choose an SRS of 49 people. a) What is the probability that the sample distribution x-bar takes values less than 190 minutes? Z= x = 190, μ = 200, o = 40, n = 49 x-μ O √n = 0.0401 z = -1.75, p = b) What is the probability that the sample distribution x-bar takes values greater than 205 minutes? Same formula as above, x = 205 z = 0.88, p = 0.8106 but "greater" so 1-0.8106 = 0.1894 c) What is the probability that the sample distribution x-bar takes values between 190 and 205 minutes? Between, subtract p-values, 0.8106 -0.0401 = 0.7705 d) What is the level L such that the probability of the mean operating times of surgeries greater than L is only 0.13? Greater than p = 0.13, so 1-0.13 = .87 FIND THE CLOSEST Z, z = 1.13 x = μ+Z = (200) + (1.13)) = 206.46 ***note: use sampling distribution***
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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Transcribed Image Text:Suppose the mean operating time of surgeries at a hospital follows N(200, 40) in minutes. Choose an SRS of 49
people.
a) What is the probability that the sample distribution x-bar takes values less than 190 minutes?
Z =
x = 190, μ = 200, o = 40, n = 49 z = -1.75, p = 0.0401
x-μ
O
√√n
b) What is the probability that the sample distribution x-bar takes values greater than 205 minutes?
Same formula as above, X = = 205
z = 0.88, p = 0.8106 but "greater" so 1-0.8106 = 0.1894
c) What is the probability that the sample distribution x-bar takes values between 190 and 205 minutes?
Between, subtract p-values, 0.8106 -0.0401 = 0.7705
d) What is the level L such that the probability of the mean operating times of surgeries greater than L is only
0.13?
Greater than p = 0.13, so 1 - 0.13 = .87 FIND THE CLOSEST Z, z = 1.13
40
/49
=
x = μ+z = (200) + (1.13)(- = 206.46 ***note: use sampling distribution***
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