i have a hard time figuring out which formula's to use when solving problems. which would i use for the following:
if X is a normal random variable with mean u=60 and a Std Dev.=2 find:
A. p(x<58)
B. p(x>63)
C. p(57<X<64)
Z = (X-μ)/SD
Look up Z values in table in back of statistics book labeled something like "areas under normal distribution."
I hope this helps. Thanks for asking.
To solve these problems, you would use the normal distribution formula or the Z-score formula. The Z-score formula is especially helpful for standardizing values and finding probabilities.
Here's how you can use the Z-score formula to solve each of the problems:
A. To find p(x < 58), you want to find the probability that the random variable X is less than 58. First, you need to standardize the value of 58 using the Z-score formula:
Z = (X - mean) / Std Dev
Z = (58 - 60) / 2
Z = -1
Once you obtain the Z-score, you can refer to the Z-table or use statistical software to find the corresponding probability. In this case, you would look up the probability associated with a Z-score of -1. The value you find represents the probability of obtaining a value less than 58.
B. To find p(x > 63), you want to find the probability that the random variable X is greater than 63. Similar to the previous problem, you need to standardize the value of 63 using the Z-score formula:
Z = (X - mean) / Std Dev
Z = (63 - 60) / 2
Z = 1.5
Once you obtain the Z-score, you can look up the probability associated with a Z-score of 1.5. This probability represents the likelihood of obtaining a value greater than 63.
C. To find p(57 < X < 64), you want to find the probability that the random variable X falls between 57 and 64. To solve this, you need to standardize both values.
For 57:
Z1 = (57 - 60) / 2
Z1 = -1.5
For 64:
Z2 = (64 - 60) / 2
Z2 = 2
Once you obtain both Z-scores, you can subtract the probability associated with the lower Z-score from the probability associated with the higher Z-score. This will give you the probability of X falling between 57 and 64.
Remember, the Z-score formula is used to standardize values and allows you to look up probabilities associated with standard normal distribution (Z-table) or use statistical software to find the corresponding probabilities.