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Answer:
Probability that next week's show will have between 30 and 37 million viewers is 0.2248.
Step-by-step explanation:
We are given that the distribution of the number of viewers for the American Idol television show follows a normal distribution with a mean of 26 million with a standard deviation of 8 million.
<em>Let X = number of viewers for the American Idol television show</em>
So, X ~ N()
Now, the z score probability distribution is given by;
Z = ~ N(0,1)
where, = population mean = 26 million
= standard deviation = 8 million
So, probability that next week's show will have between 30 and 37 million viewers is given by = P(30 < X < 37) = P(X < 37) - P(X 30)
P(X < 37) = P( <
) = P(Z < 1.38) = 0.91621
P(X 30) = P(
) = P(Z
0.50) = 0.69146
<em>Therefore, P(30 < X < 37) = 0.91621 - 0.69146 = 0.2248</em>
Hence, probability that next week's show will have between 30 and 37 million viewers is 0.2248.
Expressions do not have an equal sign (although they can have operators such as plus or minus).
is an expression.
is an equation since it has an equal sign.