E. Assuming data in the population are normally distributed with a mean (mu) of
ID: 3171970 • Letter: E
Question
E. Assuming data in the population are normally distributed with a mean (mu) of 75 and a standard deviation (sigma) of 17, determine the probability of randomly selecting a value greater than 58 and enter your response to three decimals (i.e. 0.123). Use the NORMDIST function.
F. Assuming data in the population are normally distributed with a mean (mu) of 60 and a standard deviation (sigma) of 11, determine the probability of randomly selecting a value less than 49 and enter your response to three decimals (i.e. 0.123). Use the NORMDIST function.
G. Assuming data in the population are normally distributed with a mean (mu) of 60 and a standard deviation (sigma) of 11, determine the probability of randomly selecting a value from 49 to 62 and enter your response to three decimals (i.e. 0.123). Use the NORMDIST function.
H. Assuming data in the population are normally distributed with a mean (mu) of 55 and a standard deviation (sigma) of 9, determine the value of x where the probability of a value being less is 0.25. Enter your response to two decimals (i.e. 12.34). Use the NORMINV function.
I. Calculate the value of the density function "f(x)" (formula 6.3) for a continuous uniform distribution where the minimum value (a) is 59.8 and the maximum (b) is 108.7. Enter your response to three decimals (i.e. 0.123).
J. Calculate the mean for a continuous uniform distribution with a minimum value of 73.2 and maximum of 253.1. Enter your response to one decimal (i.e. 0.1).
K. Calculate the variance for a continuous uniform distribution with a minimum value of 96.6 and maximum of 217.6. Enter your response to one decimal (i.e. 0.1).
L. Calculate the standard deviation for a continuous uniform distribution with a minimum value of 37.4 and maximum of 247.5. Enter your response to one decimal (i.e. 0.1).
M. Calculate the probability of obtaining a value greater than 174.9 for a continuous uniform distribution with a minimum value of 73.3 and maximum of 219.5. Enter your response to three decimals (i.e. 0.123).
N. Calculate the probability of obtaining a value less than 138.8 for a continuous uniform distribution with a minimum value of 13.2 and maximum of 296.4. Enter your response to three decimals (i.e. 0.123).
O. Calculate the probability of obtaining a value greater than 120 and less than 177 for a continuous uniform distribution with a minimum value of 38 and maximum of 265. Enter your response to three decimals (i.e. 0.123).
P. Assume the time it takes a mechanic to change the oil in a specific type vehicle is exponentially distributed and that the average number of oil changes for vehicles of this type, that are completed in an 8 hour shift, is 27.8. What is the average number of minutes required to complete an oil change in this type vehicle? Enter your response to one decimal (i.e. 0.1).
Q. Assume the time it takes a mechanic to change the oil in a specific type vehicle is exponentially distributed with a mean of 30.8 minutes. What is the standard deviation for the time required to complete an oil change in this type vehicle? Enter your response to one decimal (i.e. 0.1).
R. Assume the time it takes a mechanic to change the oil in a specific type vehicle is exponentially distributed with a mean of 10.6 minutes. What is the probability it will take the mechanic more than 4 minutes to change the oil in this type vehicle? Enter your response to three decimals (i.e. 0.123). Use the EXPONDIST function.
S. Assume the time it takes a mechanic to change the oil in a specific type vehicle is exponentially distributed with a mean of 11.9 minutes. What is the probability it will take the mechanic less than 4 minutes to change the oil in this type vehicle? Enter your response to three decimals (i.e. 0.123). Use the EXPONDIST function.
T. Assume the time it takes a mechanic to change the oil in a specific type vehicle is exponentially distributed with a mean of 28.8 minutes. What is the probability it will take the mechanic from 23.6 to 34.8 minutes to change the oil in a vehicle of this type? Enter your response to three decimals (i.e. 0.123). Use the EXPONDIST function.
Explanation / Answer
E.
Mean ( u ) =75
Standard Deviation ( sd )=17
Normal Distribution = Z= X- u / sd ~ N(0,1)
P(X > 58) = (58-75)/17
= -17/17 = -1
= P ( Z >-1) From Standard Normal Table
= 0.8413
F.
Mean ( u ) =60
Standard Deviation ( sd )=11
Normal Distribution = Z= X- u / sd ~ N(0,1)
P(X < 49) = (49-60)/11
= -11/11= -1
= P ( Z <-1) From Standard Normal Table
= 0.1587
G.
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 49) = (49-60)/11
= -11/11 = -1
= P ( Z <-1) From Standard Normal Table
= 0.15866
P(X < 62) = (62-60)/11
= 2/11 = 0.1818
= P ( Z <0.1818) From Standard Normal Table
= 0.57214
P(49 < X < 62) = 0.57214-0.15866 = 0.4135
H.
P ( Z < x ) = 0.25
Value of z to the cumulative probability of 0.25 from normal table is -0.674
P( x-u/s.d < x - 55/9 ) = 0.25
That is, ( x - 55/9 ) = -0.67
--> x = -0.67 * 9 + 55 = 48.9296
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