Help asap i am struggling see image for problem
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Answer:
19,656
Step-by-step explanation:
Numbers used in locker = 3
Total numbers available = 28
Repetition is not allowed, so one number can be used only once. The order of number matters in the locker e.g. 123 password is not the same as 231. Since, the order of numbers matter, this is a problem of permutations. We need to find the number of different sequences formed with 28 numbers taken 3 at a time. This can be represented as 28P3
The formula for permutations is:
For the given case, we will have:
This means, 19,656 different 3 numbered sequences are possible for the locker.
Using the normal distribution, there is a 0.4826 = 48.26% probability that the sample mean is between 15 and 16 grams per day.
<h3>Normal Probability Distribution</h3>The z-score of a measure X of a normally distributed variable with mean and standard deviation
is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation
.
For this problem, the parameters are given as follows:
The probability is the <u>p-value of Z when X = 16 subtracted by the p-value of Z when X = 15</u>, hence:
X = 16:
By the Central Limit Theorem
Z = 2.11
Z = 2.11 has a p-value of 0.9826.
X = 15:
Z = 0
Z = 0 has a p-value of 0.5.
0.9826 - 0.5 = 0.4826 = 48.26% probability that the sample mean is between 15 and 16 grams per day.
More can be learned about the normal distribution at brainly.com/question/15181104
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