Assuming that the “age” variable for the individuals in the Patients\' dataset i
ID: 3316153 • Letter: A
Question
Assuming that the “age” variable for the individuals in the Patients' dataset is normally distributed, what is the probability that the age of a patient in this dataset:
Is less than 45?
Is greater than 55?
Lies between 45 and 55?
Age (Years) 78 74 89 81 87 65 90 61 90 78 78 71 76 76 79 72 72 64 72 69 63 78 83 62 71 83 63 83 76 79 65 79 74 63 84 90 73 81 75 87 70 73 77 71 76 49 78 86 67 69 73 88 67 69 77 64 76 64 41 49 59 81 74 77 78 73 67 80 77 73 67 86 82 84 73 82 62 84 89 84 81 81 78 84 37 62 80 80 73 80 80 80 81 39 86 79 87 53 83 80 79 72 77 81 67 80 67 88 88 92 85 85 80 98 74 77 53 93 83 80 79 87 59 81 94 33 78 29 80 63 86 96 89 80 55 73 67 75Explanation / Answer
The mean of the sample is = 74.91
The standard deviation is 12.12
the probability that the age of a patient in this dataset is less than 45
i.e P(X<45)= 0.0067 ## Using R command >pnorm(45,74.91,12.12)
the probability that the age of a patient in this dataset is greter than 55
P(X>55) = 1- P(X<55)
= 0.9497 ## Using > 1 - pnorm(55,74.91,12.12)
the probability that the age of a patient in this dataset is between 45 and 55
P(45<X<55) = P(X<55)- P(X<45)
= 0.0434 ## pnorm(55,74.91,12.12) - pnorm(45,74.91,12.12)