repost
MEAN=10 & STANDARD DEVIATION =2. FIND THE PROBABILITIES:
9.4 �less than X less than 10.6
i have 2 different answers but am checking the answer. thank you
one is 0.6179
the other is 0.2358
one of the best on the web for this
http://davidmlane.com/hyperstat/z_table.html
enter mean--10, SD --- 2
click on between, enter 9.4 and 10.6
it gave me .235823
thank you reiny that's one of my answers ...
To find the probability of a given range of values in a normal distribution, you need to convert those values into standardized z-scores using the formula:
z = (X - mean) / standard deviation
In this case, you want to find the probability for the range between 9.4 and 10.6.
Step 1: Calculate the z-score for the lower value, 9.4.
z1 = (9.4 - 10) / 2
z1 = -0.3 / 2
z1 = -0.15
Step 2: Calculate the z-score for the upper value, 10.6.
z2 = (10.6 - 10) / 2
z2 = 0.6 / 2
z2 = 0.3
Step 3: Look up the corresponding probabilities for the z-scores using the standard normal distribution table or a calculator.
The probability of being less than both z1 and z2 is 0.2358.
Keep in mind that this value represents the probability from negative infinity to z2, not from z1 to z2.
Therefore, the correct answer is 0.2358, not 0.6179.