Answer :
To determine the probabilities for the given normal distribution problems using the NORM.DIST function in Excel, we can follow these steps:
a. μ = 780,
σ = 66.9,
x ≤ 842
The formula used would be:
=NORM.DIST(842, 780, 66.9, TRUE)
b. μ = 83,
σ = 19,
x < 56
The formula used would be:
=NORM.DIST(56, 83, 19, TRUE)
c. μ = 211,
σ = 43.5,
190 ≤ x < 276
To find the probability in the given range, we need to subtract the probability of x < 190 from the probability of x < 276. The formulas used would be:
=NORM.DIST(190, 211, 43.5, TRUE) - NORM.DIST(276, 211, 43.5, TRUE)
d. μ = 168,
σ = 7.9,
156 < x < 162
To find the probability in the given range, we need to subtract the probability of x < 156 from the probability of x < 162. The formulas used would be:
=NORM.DIST(156, 168, 7.9, TRUE) - NORM.DIST(162, 168, 7.9, TRUE)
e. μ = 52,
σ = 4.35,
x > 46
To find the probability for x > 46, we subtract the probability of x < 46 from 1 (since the sum of all probabilities is 1). The formula used would be:
=1 - NORM.DIST(46, 52, 4.35, TRUE)
f. μ = 233,
σ = 14.4,
x ≥ 250
To find the probability for x ≥ 250, we subtract the probability of x < 250 from 1. The formula used would be:
=1 - NORM.DIST(250, 233, 14.4, TRUE) . By plugging in the appropriate values into the NORM.DIST function in Excel, we can determine the probabilities for the given normal distribution problems. The formulas used for each problem are provided above.
To find the probabilities, we need to use the NORM.DIST function in Excel, which calculates the cumulative distribution function (CDF) for a given normal distribution. The function requires four arguments: the value at which we want to evaluate the distribution (x), the mean (μ), the standard deviation (σ), and a logical value that determines whether we want to calculate the cumulative probability (TRUE) or the probability density function (FALSE).
For each problem, we use the appropriate formula to calculate the probability. For example, in problem a, we use the formula =NORM.DIST(842, 780, 66.9, TRUE). This calculates the probability of getting a value less than or equal to 842 in a normal distribution with a mean of 780 and a standard deviation of 66.9.
Conclusion:
By using the NORM.DIST function in Excel, we can calculate the probabilities for the given normal distribution problems. The formulas provided in the steps above can be used to determine the probabilities for each problem.
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