= 0.3133
Given: μ = 560
σ = 90
To find: P (490 < X < 560)
Normal distributions are symmetric, unimodal, and asymptotic. A normal distribution is determined by two parameters the mean and the variance. A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution. It's always easy to solve questions in terms to standard normal
Hence, converting normal distribution to standard normal gives:
P(490 < X < 560) = ≤
= P(0 ≤ Z < 0.888)
= P (z<0.89) - P(z ≤ 0)
Using standard normal table,
= 0.8133 - 0.5
P(490 < X < 560) = 0.3133
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The first 5 terms in an arithmetic sequence is 4,2,0,-2,-4
Explanation:
The general form of an arithmetic sequence is
where a denotes the first term of the sequence, d denotes the common difference.
Here a = 4 and d = -2
To determine the consecutive terms of the sequence, let us substitute the values for n.
To find the second term, substitute n = 2 in the formula
Simplifying,
Similarly,
For n = 3,
For n = 4,
For n = 5,
Thus, the first 5 terms of the arithmetic sequence is 4,2,0,-2,-4