Alex rolls a six-sided number cube 570 times. Approximately how many times can he expect to roll a 5?
2 answers:
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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 .
Answer:
Difference between the original and current volumes = 4013140.30 cubic feet
Step-by-step explanation:
Largest pyramid has the square base with one edge = 754 feet
Area of the square base = (Side)²
= (754)²
= 568516 square feet
Volume of the pyramid =
=
= 91152065.3 cubic feet
After erosion,
Area of the base = (745)² = 555025 square feet
Volume of the pyramid =
= 87138925 cubic feet
Difference between the original and current volumes of the pyramid
= 91152065.30 - 87138925
= 4013140.30 cubic feet