To determine the variance, we need to first calculate the second moment as follows: The variance can be determined using this equation: The standard deviation is simply the square root of the variance, which gives us the result.
Answer:
(A) 0.15625
(B) 0.1875
(C) Cannot be determined
Step-by-step explanation:
The time it takes for a student to finish a statistics quiz is uniformly distributed between 32 and 64 minutes.
Let's denote X as the duration needed for the student to complete the statistics quiz
Thus, X ~ U(32, 64)
The probability density function (PDF) for a uniform distribution is expressed as;
f(X) =
, a < X < b where a = 32 and b = 64
The cumulative distribution function (CDF) is given by P(X <= x) =
(A) The probability of a student taking longer than 59 minutes to complete the quiz = P(X > 59)
P(X > 59) = 1 - P(X <= 59) = 1 -
= 1 -
=
= 0.15625
(B) The probability that a student completes the quiz between 37 and 43 minutes = P(37 <= X <= 43) = P(X <= 43) - P(X < 37)
P(X <= 43) =
=
= 0.34375
P(X < 37) =
=
= 0.15625
P(37 <= X <= 43) = 0.34375 - 0.15625 = 0.1875
(C) The probability that a student takes exactly 44.74 minutes to complete the quiz
= P(X = 44.74)
This probability cannot be calculated as it is a continuous distribution, which doesn't provide probabilities for specific points.
The diagram below illustrates the issue at hand.
Question 1:
The maximum area of the pool equals half the area of the circle.
To calculate the area of the circle: Area = πr², with r being half of the diameter.
Thus, Area of circle = π(60)² = 11309.73355 square feet.
Therefore, the area representing half the circle amounts to 11309.73355/2 = 5654.866... ≈ 5654.87 square feet (rounded to 2 decimal places).
Question b:
To find the pool's area, we take the circle's area and subtract the triangle's area.
The area of the circle is 11309.73 square feet.
For the triangle's area calculation: 1/2 × (60×103.92) = 3117.6 square feet.
The area of the pool thus operates as 11309.73 - 3117.6 = 7922.13 square feet.
Calculating the pool's volume: 7922.13 × 4 = 31688.52 cubic feet.
Note: Information related to the fish tank is unavailable, so the above calculation focuses solely on the entire pool's volume.
Answer:
5 miles in total
Step-by-step explanation:
Given:
Time spent driving = 10 min = 10 / 60 = 1/6 hour
Duration of stop = 5 min
Driving speed = 30 miles per hour
Find:
Complete distance
Computation:
Distance traveled = Speed × time
Distance = 30 × (1/6)
Total distance = 5 miles