30 new babies were born yesterday in the hospital. If the average weight of a new born is 7.5 pounds with a standard deviation of 2.1 pounds, what is the probability of the average weight for these 30 newborns is between 7.2 and 7.6 pounds. Remember, all probabilities are taken to 4 decimal places for this class
Z = (score-mean)/SEm
SEm = SD/√n
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability between the two Z scores.
To find the probability of the average weight for these 30 newborns falling between 7.2 and 7.6 pounds, we need to use the properties of the normal distribution.
Step 1: Standardize the values
First, we need to standardize the given weights using the formula:
z = (x - μ) / σ
where:
x = given weight
μ = mean weight
σ = standard deviation
Let's calculate the z-scores for 7.2 and 7.6:
For 7.2 pounds:
z1 = (7.2 - 7.5) / 2.1
For 7.6 pounds:
z2 = (7.6 - 7.5) / 2.1
Step 2: Look up the z-scores in the z-table
Next, we need to look up the z-scores from step 1 in the z-table. The z-table provides the probability corresponding to a given z-score.
Let's assume we obtain z1_prob for z1 and z2_prob for z2 from the z-table.
Step 3: Calculate the final probability
Now, we can calculate the probability of the average weight being between 7.2 and 7.6 pounds using the following formula:
probability = z2_prob - z1_prob
This is because the values in the z-table represent the area under the standard normal curve. By subtracting the cumulative probabilities of the two z-scores, we get the probability of the average weight falling between those values.
Note: Since all probabilities are taken to 4 decimal places, make sure to round the final probability to 4 decimal places.
To obtain the precise value, you will need access to a z-table or a statistical software that can provide the probability directly.