ASSUME THE THE MEAN WEIGHT OF CHILDREN AGES 7 IS 50 POUNDS AND A STANDARD DEVIATION OF 10. wHAT IS THE PROBABLITY THAT A RANDOM SELECTED 7 YEAR OLD WILL HAVE A WEIGHT THAT IS LESS THAT 65
You have to find the z-score.
65-50 = 15 then divide by 10 which is z = 1.5
You can then use a z-table or a stat calculator to find the probablity less than 65%
Depending on the table, you may want to find the probability of z = 1.5 or greater and then subtract that number from 1 to get the less than.
For a normal distribution, what is the probability of randomly selecting a z score greater than Z=- 2.0
To find the probability that a randomly selected 7-year-old child will have a weight less than 65 pounds, we can use the Z-score formula and then look up the corresponding probability in the standard normal distribution table.
Step 1: Calculate the Z-score:
The Z-score formula is given by: Z = (X - μ) / σ
Where:
X = 65 pounds (the weight we want to find the probability for)
μ = 50 pounds (mean weight of children ages 7)
σ = 10 pounds (standard deviation)
Z = (65 - 50) / 10
Z = 15 / 10
Z = 1.5
Step 2: Look up the probability associated with the Z-score:
Using the standard normal distribution table or a calculator, we can find the area under the curve to the left of the Z-score of 1.5 (since we want the probability of a weight less than 65 pounds).
From a standard normal distribution table, we find that the cumulative probability for a Z-score of 1.5 is approximately 0.9332 or 93.32%.
Therefore, the probability that a randomly selected 7-year-old child will have a weight less than 65 pounds is approximately 93.32%.
To find the probability that a randomly selected 7-year-old child will have a weight less than 65 pounds, we can use the standard deviation and mean weight information given.
First, we need to convert the information into a standardized form by calculating the z-score. The z-score measures how many standard deviations a value is from the mean and allows us to use a standard normal distribution table.
The formula for calculating the z-score is:
z = (x - μ) / σ
where:
x = desired weight (65 pounds)
μ = mean weight (50 pounds)
σ = standard deviation (10 pounds)
Let's calculate the z-score:
z = (65 - 50) / 10
z = 15 / 10
z = 1.5
Next, we need to find the probability of a z-score less than 1.5 using a standard normal distribution table or calculator. The table provides the cumulative probability up to a certain z-score.
By looking up the z-score of 1.5 in the standard normal distribution table, we can find the corresponding probability.
The table will give us the value 0.9332 for a z-score of 1.5.
This means that approximately 93.32% of children's weights will be less than 65 pounds.
Therefore, the probability that a randomly selected 7-year-old child will have a weight less than 65 pounds is approximately 0.9332 or 93.32%.