The random variable, X, has a normal distribution with mean 12 and standard deviation 0.25. If the random variable, Z, has the standard normal distribution, then the probability that X is greater than 13 is equal to what probability of Z?
| 11.75 | 12 | 12.25 | 12.5 | 12.75 | 13 |
|---|---|---|---|---|---|
| -1 | 0 | 1 | 2 | 3 | 4 |
Let X be a normally distributed random variable, with a mean of 15. If the standard deviation is a third of the mean value, find the approximate value of Pr(10≤X≤25).
| 10 | 15 | 20 | 25 | 30 |
|---|---|---|---|---|
| -1 | 0 | 1 | 2 | 3 |
Pr(10≤X≤25) = 0.682+0.136=0.818
Suppose X is normally distributed with mean μ=50 and standard deviation σ=10, Z is a standard normal random variable. Pr(−2.5<Z<1.5) is equal to what probability of X?
| -2.5 | -1.5 | -0.5 | 0.5 | 1.5 | 2.5 |
|---|---|---|---|---|---|
| 25 | 35 | 45 | 55 | 65 | 75 |
Pr(−2.5<Z<1.5) = Pr(25<X<65) = Pr(35<X<75)
The average amount of time a year 12 student sleeps for at night is 7 hours with a variance of b hours. Given that the probability a student sleeps for more than 9 hours is the same as Pr(Z<−1), where Z is the standard normal random variable, find the value of b.
| 7 | ||||
|---|---|---|---|---|
| -1 | 0 | 1 | 2 | 3 |
Pr(Z<−1) = Pr() = Pr(X>9)
Let X be a normally distributed random variable, with a mean of 100 and a standard deviation of 34. Find Pr(X≤134)
| 100 | 134 |
|---|---|
| 0 | 1 |
Pr(X≤134) = Pr(Z≤1) = 0.997/2 + 0.34 = 0.8413
Suppose X is normally distributed with mean μ=20 and standard deviation σ=4, Z is a standard normal random variable. Find the value of b such that Pr(X≤12)=Pr(Z>b).
| 12 | 16 | 20 | 24 | 28 |
|---|---|---|---|---|
| -2 | -1 | 0 | 1 | 2 |
Pr(X≤12) = Pr(X<12) = Pr(Z>b) = Pr(Z←2) = Pr(Z>2)
The random variable, X, has a normal distribution with mean 12 and standard deviation 0.25. If the random variable, Z, has the standard normal distribution, then the probability that X is greater than 12.5 is equal to what probability of Z?
| 11.5 | 12 | 12.5 | 13 |
|---|---|---|---|
| -2 | 0 | 2 | 4 |
Pr(X>12.5) = Pr(Z>2)
The random variable X has a normal distribution with mean 148 and standard deviation 12. If Z has the standard normal distribution, then the probability that Z is less than −2.5 is equal to:
| 118 | 136 | 148 | 160 |
|---|---|---|---|
| -2.5 | -1 | 0 | 1 |
Pr(Z←2.5) = Pr(X<118) = Pr(X>178)
Assume that X is a normally distributed random variable with mean μ=1 and variance σ2=2.25. If Pr(μ−k<X<μ+k)=0.7, what is k?
| -1 | 2 | 5 | ||
|---|---|---|---|---|
| -k | -1 | 0 | 1 | k |
We know that
Inverse Normal: 0.1 is the area under Z between
Therefore