A smaller square is within a larger square as shown below. A point is chosen at random in the larger square. What percent of the
time will be in the BLUE region? Round to the nearest tenth of a percent.
1 answer:
Answer: 84.5%
Step-by-step explanation:
15.2 × 15.2 = 231.04 cm² (area of the entire large square)
5.98 × 5.98 = 35.76 cm² (area of the small square)
large square - small square = area of the blue region
231.04 - 35.76 = 195.28 cm² (area of the blue region)
= percentage of time that the point will be in the blue region
= 0.845 --> 84.5%
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Answer:
Probability that the sample average is at most 3.00 = 0.98030
Probability that the sample average is between 2.65 and 3.00 = 0.4803
Step-by-step explanation:
We are given that the sediment density (g/cm) of a randomly selected specimen from a certain region is normally distributed with mean 2.65 and standard deviation 0.85.
Also, a random sample of 25 specimens is selected.
Let X bar = Sample average sediment density
The z score probability distribution for sample average is given by;
Z = ~ N(0,1)
where, = population mean = 2.65
= standard deviation = 0.85
n = sample size = 25
(a) Probability that the sample average sediment density is at most 3.00 is given by = P( X bar <= 3.00)
P(X bar <= 3) = P( <=
) = P(Z <= 2.06) = 0.98030
(b) Probability that sample average sediment density is between 2.65 and 3.00 is given by = P(2.65 < X bar < 3.00) = P(X bar < 3) - P(X bar <= 2.65)
P(X bar < 3) = P( <
) = P(Z < 2.06) = 0.98030
P(X bar <= 2.65) = P( <=
) = P(Z <= 0) = 0.5
Therefore, P(2.65 < X bar < 3) = 0.98030 - 0.5 = 0.4803 .