Answer:
Probability that in a given week, the profits will be between 8 and 10.5 million dollars is 0.3674.
Step-by-step explanation:
We are given that the Massachusetts State Lottery averages, on a weekly basis, a profit of 10.0 million dollars. The variability, as measured by the variance statistic is 6.25 million dollars squared.
Also, it is known that the weekly profits is distributed normally.
Firstly, <em>Let X = weekly profits</em>
The z score probability distribution for is given by;
Z = ~ N(0,1)
where, = population mean profit = 10 million dollars
= standard deviation =
=
= 2.5 million dollars
Probability that, in a given week, the profits will be between 8 and 10.5 million dollars is given by = P(8 < X < 10.5) = P(X < 10.5) - P(X 8)
P(X < 10.5) = P( <
) = P(Z < 0.2) = 0.57926
P(X 8) = P(
) = P(Z
-0.8) = 1 - P(Z < 0.8)
= 1 - 0.78814 = 0.21186
Therefore, P(8 < X < 10.5) = 0.57926 - 0.21186 = 0.3674
Hence, the chances that, in a given week, the profits will be between 8 and 10.5 million dollars is 0.3674.