A six sided cube is rolled. find the probability of P (4) as a decimal
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You use the arithmetic sequence formula and input the information given to you.
tn = a + (n-1)d
t(56) is what your looking for so don't worry about the tn.
a is your first term,
a = 15.
n is the position of the term you are looking for, n = 56.
And d is the common difference, you find this by taking t2 and subtracting t1. t2=18 and t1=15.
d = 18 - 15 = 3
Inputting it all into the formula you get,
t(56) = 15 + (56-1)(3)
term 56 = 180.
You use this formula to find any term in a sequence provided you are given enough info. You can also manipulate it if you are asked to find something else like the first term(a), common difference(d) or term position(n). It just depends on what the question is asking and what information you are given. :)
Hope this helps!
tn = a + (n-1)d
t(56) is what your looking for so don't worry about the tn.
a is your first term,
a = 15.
n is the position of the term you are looking for, n = 56.
And d is the common difference, you find this by taking t2 and subtracting t1. t2=18 and t1=15.
d = 18 - 15 = 3
Inputting it all into the formula you get,
t(56) = 15 + (56-1)(3)
term 56 = 180.
You use this formula to find any term in a sequence provided you are given enough info. You can also manipulate it if you are asked to find something else like the first term(a), common difference(d) or term position(n). It just depends on what the question is asking and what information you are given. :)
Hope this helps!
Answer:
The probability that the shopkeeper's annual profit will not exceed $100,000 is 0.2090.
Step-by-step explanation:
According to the Central Limit Theorem if we have a population with mean <em>μ</em> and standard deviation <em>σ</em> and we select appropriately huge random samples (<em>n</em> ≥ 30) from the population with replacement, then the distribution of the sum of values of <em>X</em>, i.e ∑<em>X</em>, will be approximately normally distributed.
Then, the mean of the distribution of the sum of values of X is given by,
And the standard deviation of the distribution of the sum of values of X is given by,
The information provided is:
<em>μ</em> = $970
<em>σ</em> = $129
<em>n</em> = 102
Since the sample size is quite large, i.e. <em>n</em> = 102 > 30, the Central Limit Theorem can be used to approximate the distribution of the shopkeeper's annual profit.
Then,
Compute the probability that the shopkeeper's annual profit will not exceed $100,000 as follows:
*Use a <em>z</em>-table for the probability.
Thus, the probability that the shopkeeper's annual profit will not exceed $100,000 is 0.2090.