http://psych.colorado.edu/~mcclella/java/normal/accurateNormal.html
Put the mean, and the standard deviation in the top of the applet.
Having a lot of trouble with this one problem...any help would be appreciated
The weight of the eggs produced by a certain breed of hen is normally distributed with mean 65 grams and stdDev 5 grams. Think of these cartons of eggs as SRSs of size 12 from the population of all eggs. What is the prob. that the weight of the carton falls between 750 g and 825 g?
To solve this problem, we need to find the probability that the weight of the carton falls between 750 g and 825 g, given the mean weight of 65 grams and a standard deviation of 5 grams.
To begin, let's calculate the mean and standard deviation for a single egg in the carton. Since these cartons contain a simple random sample (SRS) of size 12, the mean weight of an egg will still be 65 grams, but the standard deviation will be 5 grams divided by the square root of 12 (as the standard deviation for the sample mean is equal to the population standard deviation divided by the square root of the sample size).
So, the standard deviation for a single egg in the carton would be:
Single Egg Standard Deviation = 5 grams / √12 ≈ 1.44 grams
Next, we can convert the weight range from 750 g - 825 g to z-scores, which represent the number of standard deviations a given value is from the mean in a normal distribution. We can use the formula:
z = (x - μ) / σ
where z is the z-score, x is the value (750 g or 825 g), μ is the mean (65 grams), and σ is the standard deviation (1.44 grams).
For the lower bound:
z lower = (750 g - 65 grams) / 1.44 grams ≈ 499.31
For the upper bound:
z upper = (825 g - 65 grams) / 1.44 grams ≈ 529.86
Now, we need to find the area under the normal distribution curve between these two z-scores. This represents the probability of the weight of the carton falling between 750 g and 825 g.
To calculate this probability, we can use a standard normal distribution table or a calculator. However, since you provided a link to an applet, you can input the mean (65 grams) and the standard deviation (1.44 grams) into the applet you shared (http://psych.colorado.edu/~mcclella/java/normal/accurateNormal.html) and enter the z-scores (499.31 and 529.86) to find the probability directly.
By inputting the mean, standard deviation, and the z-scores into the applet, it will give you the probability that the weight of the carton falls between 750 g and 825 g.