Z is a standard normal random variate. For Pr(c < Z) = 0.278, what is the value for c?
You can find this by using a z-table. The .278 is in the body, find the value for c by using the margins.
or you can use a graphing calculator.
2nd vars invNorm(.278)
To find the value of c given Pr(c < Z) = 0.278, we need to use the cumulative distribution function (CDF) of the standard normal distribution.
The CDF of a standard normal distribution gives the probability that a standard normal random variable is less than or equal to a given value (in this case, c).
However, the provided probability Pr(c < Z) represents the probability that the standard normal random variable Z is LESS than c, not less than or equal to c. Therefore, we need to subtract this probability from 1 to find Pr(Z < c).
Pr(Z < c) = 1 - Pr(c < Z) = 1 - 0.278 = 0.722.
To find the value of c that corresponds to Pr(Z < c) = 0.722, we can use a standard normal distribution table or a statistical calculator.
Using a standard normal distribution table, look up the value closest to 0.722. The closest value is approximately 0.714. The corresponding value of c can be found in the table as the Z-score.
So, c ≈ 0.714.
Alternatively, you can use a statistical calculator or software to calculate the inverse of the standard normal CDF at 0.722. This will directly give you the value of c without looking it up in a table.