The birth weight of full-term babies was found to follow a normal distribution with a mean of 3500grams, and standard deviation of 600grams.
A) What is probability that the birth weight is less than 3000 grams.
= P(X<3000) Correct?
B) probability that birth weight exceeds 4000grams P(X>4000) Correct?
C) birth weight between 3000 and 4000
P(3000<X>4000) Correct?
D) This one confuses me
birth weight less than 2000 OR greater than 5000????
http://davidmlane.com/hyperstat/z_table.html
D -- add the percent < 2000 to the percent > 5000
LOL or subtract the percent between 2000 and 5000 from 100 :)
Correct as far as you went, but what are the probabilities?
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability
related to the Z scores.
D) Either-or probabilities are found by adding the individual probabilities.
When I say percent I men probability = percent/100
The z table is at that David Lane link
A) To find the probability that the birth weight is less than 3000 grams, we need to calculate P(X < 3000) where X follows a normal distribution with a mean of 3500 grams and a standard deviation of 600 grams.
To solve this, we can standardize the value using the z-score formula:
z = (X - mean) / standard deviation
Applying this formula, we get:
z = (3000 - 3500) / 600 = -0.8333
To find the probability, we look up the z-score in the standard normal distribution table (also known as the Z-table) or use a calculator that can calculate the cumulative distribution function (CDF) for a given value of z.
Using the Z-table, we look up the z-value of -0.8333, which corresponds to a probability of 0.2033.
Therefore, the probability that the birth weight is less than 3000 grams is 0.2033, or 20.33%.
B) To find the probability that the birth weight exceeds 4000 grams, we need to calculate P(X > 4000), where X follows a normal distribution with a mean of 3500 grams and a standard deviation of 600 grams.
Similar to the previous question, we standardize the value using the z-score formula:
z = (X - mean) / standard deviation
Using this formula, we get:
z = (4000 - 3500) / 600 = 0.8333
Again, we can consult the Z-table or use a calculator to find the probability corresponding to a z-value of 0.8333.
Looking up the z-value of 0.8333 in the Z-table, we find a probability of 0.7967. Therefore, the probability that the birth weight exceeds 4000 grams is 0.7967, or 79.67%.
C) To find the probability that the birth weight is between 3000 and 4000 grams, we want to calculate P(3000 < X < 4000), where X follows a normal distribution with a mean of 3500 grams and a standard deviation of 600 grams.
To solve this, we need to find the probabilities separately for both ends and subtract them to get the desired range.
First, calculate P(X < 4000):
Using the same standardization formula, we get:
z = (4000 - 3500) / 600 = 0.8333
Consulting the Z-table or using a calculator, we find that the probability corresponding to a z-value of 0.8333 is 0.7967.
Next, calculate P(X < 3000):
z = (3000 - 3500) / 600 = -0.8333
Looking up the z-value of -0.8333 in the Z-table, we find a probability of 0.2033.
Finally, subtract the two probabilities to find the range in between:
P(3000 < X < 4000) = P(X < 4000) - P(X < 3000)
= 0.7967 - 0.2033
= 0.5934 or 59.34%.
D) To find the probability that the birth weight is either less than 2000 grams or greater than 5000 grams, we need to calculate P(X < 2000) or P(X > 5000).
For P(X < 2000):
Using the same standardization formula, we get:
z = (2000 - 3500) / 600 = -2.5
Looking up the z-value of -2.5 in the Z-table, the probability is approximately 0.0062 or 0.62%.
For P(X > 5000):
Using the same standardization formula:
z = (5000 - 3500) / 600 = 2.5
Looking up the z-value of 2.5 in the Z-table, the probability is approximately 0.9938 or 99.38%.
To find the combined probability, we can add the probabilities for the mutually exclusive events:
P(X < 2000) or P(X > 5000) = P(X < 2000) + P(X > 5000)
= 0.0062 + 0.9938
= 1 or 100%.
So, the probability that the birth weight is either less than 2000 grams or greater than 5000 grams is 100%, which makes sense as it includes all possible outcomes outside the given range.