Let’s say the random variable X is normally distributed with µ = 35 and σ = 5. Find P(25 < X < 50), i.e., the probability of the variable taking a value between 25 and 50. (Report the answer as a number rounded off to two digits after the decimal point.)Note: You’re not expected to know the right answer at this point. This question is given just to get you thinking in the right direction.
Question
Let’s say the random variable X is normally distributed with µ = 35 and σ = 5. Find P(25 < X < 50), i.e., the probability of the variable taking a value between 25 and 50. (Report the answer as a number rounded off to two digits after the decimal point.)Note: You’re not expected to know the right answer at this point. This question is given just to get you thinking in the right direction.
Solution
To solve this problem, we need to convert the raw scores to z-scores and then look up the corresponding probabilities in the standard normal distribution table.
Step 1: Convert the raw scores to z-scores. The formula for converting a raw score to a z-score is:
Z = (X - µ) / σ
For X = 25, the z-score is:
Z = (25 - 35) / 5 = -2
For X = 50, the z-score is:
Z = (50 - 35) / 5 = 3
Step 2: Look up the corresponding probabilities in the standard normal distribution table.
The probability for Z = -2 (P(Z < -2)) is 0.0228, and the probability for Z = 3 (P(Z < 3)) is 0.9987.
Step 3: Subtract the two probabilities to find the probability of the variable taking a value between 25 and 50.
P(25 < X < 50) = P(Z < 3) - P(Z < -2) = 0.9987 - 0.0228 = 0.9759
So, the probability of the variable taking a value between 25 and 50 is approximately 0.98 (rounded off to two digits after the decimal point).
Similar Questions
Let’s say the random variable X is normally distributed with a mean (µ) = 35 and standard deviation (σ) = 5. Can you find P(25 < X < 45), i.e., the probability of the variable falling between 25 and 45? Note 1: Report the answer as a number rounded off to two digits after the decimal point.Note 2: You’re not expected to know the right answer at this. This question is given just to get you thinking in the right direction
Probability of Normal Random VariablesLet’s say that you need to find the cumulative probability for a random variable X which is normally distributed. You do not know what the value of X is or, for that matter, what the value of µ and σ is. You only know that X = µ + σ. Can you find the cumulative probability, i.e. the probability of the variable being less than µ + σ?
A RANDom variable X is normally distributed with mean 20 and standard deviation 4. find: a) P(X>25) B)P(X<25) C)The value of d such that P(20<X<D)=0.4641 D)P(15 "LESS THAN OR EQUAL TO" X "LESS THAN OR EQUAL TO 20"
A normally distributed random variable X is converted to Z. Find P(−2 < Z < 3). Note: Report the answer as a number rounded off to two digits after the decimal point.
What is the probability that a normal random variable will take a value that is less than 1.05 standard deviations above its mean? In other words, what is P(Z < 1.05)?0.85310.14680.93320.0668What is the probability that a normal random variable will take a value that is between 1.5 standard deviations below the mean and 2.5 standard deviations above the mean? In other words, what is P(−1.5 < Z < 2.5)?0.99380.06680.92700.0730What is the probability that a normal random variable will take a value that is more than 2.55 standard deviations above its mean? In other words, what is P(Z > 2.55)?0.99450.99460.00550.0054
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.