(2 thousands 7 tens) times 10
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Given Information:
John's mean monthly commission = μ = $10,000
Standard deviation of monthly commission = σ = $2,000
Answer:
The probability that John's commission from the jewelry store is between $9,000 and $11,000 is 38.3%
Step-by-step explanation:
What is Normal Distribution?
We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.
We want to find out the probability that John's commission from the jewelry store is between $9,000 and $11,000?
The z-score corresponding to 0.50 is 0.6915
The z-score corresponding to -0.50 is 0.3085
Therefore, the probability that John's commission from the jewelry store is between $9,000 and $11,000 is 38.3%
How to use z-table?
Step 1:
In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 1.4, 2.2, 0.5 etc.)
Step 2:
Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 0.50 then go for 0.00 column)
Step 3:
Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.
Answer:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the scores for the univerisity A, and we know that:
Let Y the scores for the univerisity B, and we know that:
We select a sample size of size n=2, and since the distirbution for X is normal then the distribution for the sample mean would be given by:
And for the univeristy B we select a sample of n=3
Since both sample means are normally distributed then the difference is also normal distributed with the following parameters:
And we want this probability:
And we can use the z score given by:
And if we replace we got :
And if we find the probability using the normla standard table or excel we got:
Given :
Time they traveled in a day , .
Average speed , .
To Find :
How far did they hike altogether in 4 days .
Solution :
We know , distance covered is given by :
So , distance covered in 4 days is :
Therefore , distance they hike in 4 days is 38.5 miles .
Hence , this is the required solution .