the weights of newborn babies are distributed normally, with the mean of approximately 115 oz and a standard deviation of 20 oz. if a newborn baby is selected at random. what is the probability that the baby weighs more than 95 oz?
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 score.
To find the probability that a randomly selected newborn baby weighs more than 95 oz, we need to find the area under the normal curve to the right of 95 oz.
First, let's use the given information about the mean and standard deviation of the weights:
Mean (μ): 115 oz
Standard Deviation (σ): 20 oz
We can calculate the Z-score for 95 oz, which measures how many standard deviations below or above the mean a given value is. The formula to calculate the Z-score is:
Z = (X - μ) / σ
Where X is the value we want to find the Z-score for (95 oz in this case). Substituting the given values into the formula, we have:
Z = (95 - 115) / 20
Z = -20 / 20
Z = -1
Now, we need to find the proportion (probability) of the area under the normal curve to the right of this Z-score (Z > -1). We can use a Z-table or a statistical calculator to find this probability.
Using a Z-table, we can find the proportion associated with a Z-score of -1. The table provides the cumulative probability up to a given Z-score. In this case, we want the proportion to the right of -1, which is 1 minus the cumulative probability up to -1.
Looking up the Z-score of -1 in the Z-table, we find that the cumulative probability up to -1 is approximately 0.1587. Therefore, the probability to the right of -1 is:
P(Z > -1) = 1 - 0.1587
P(Z > -1) ≈ 0.8413
So, the probability that a randomly selected newborn baby weighs more than 95 oz is approximately 0.8413, or 84.13%.
To find the probability that a randomly selected newborn baby weighs more than 95 oz, we need to calculate the Z-score and then find the corresponding area under the standard normal distribution curve.
The Z-score formula is given by:
Z = (X - μ) / σ
Where:
X = the value (95 oz)
μ = the mean (115 oz)
σ = the standard deviation (20 oz)
Let's calculate the Z-score first:
Z = (95 - 115) / 20
Z = -20 / 20
Z = -1
Next, we need to find the area under the standard normal distribution curve to the right of Z = -1. This area represents the probability that a baby weighs more than 95 oz.
Using a Z-table or a statistical calculator, we find that the area to the right of Z = -1 is approximately 0.8413.
Therefore, the probability that a newborn baby weighs more than 95 oz is approximately 0.8413 or 84.13%.