Josh is planning a trip over the summer to New York for three nights and four days with 7 of his friends. He wants to estimate t
1 answer:
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The hexagon divides the circle into 6 parts. That means the angle projecting each side is: 360°÷ 6 = 60°
The area of a circle is: πr²
78.54 in² divided by pi is 25 making the radius = 5
I would then use SOH CAH TOA to solve for the side.. knowing the hypotenuse is the radius and the angle to split it into a right triangle is 30°
Sin(30) = s/5
5*Sin(30) = s
12*s = perimeter hexagon
(remember s is half the hexagon side)
12*5*Sin(30) = perimeter hexagon
30 inches = perimeter
The area of a circle is: πr²
78.54 in² divided by pi is 25 making the radius = 5
I would then use SOH CAH TOA to solve for the side.. knowing the hypotenuse is the radius and the angle to split it into a right triangle is 30°
Sin(30) = s/5
5*Sin(30) = s
12*s = perimeter hexagon
(remember s is half the hexagon side)
12*5*Sin(30) = perimeter hexagon
30 inches = perimeter
Answer:
(a) X ~ N().
~ N(
).
(b) If a single randomly selected individual is observed, the probability that this person consumes is between 61.4 mL and 62.8 mL is 0.0398.
(c) For the group of 43 pancake eaters, the probability that the average amount of syrup is between 61.4 mL and 62.8 mL is 0.2512.
(d) Yes, for part (d), the assumption that the distribution is normally distributed necessary.
Step-by-step explanation:
We are given that the amount of syrup that people put on their pancakes is normally distributed with mean 63 mL and a standard deviation of 13 mL.
Suppose that 43 randomly selected people are observed pouring syrup on their pancakes.
(a) Let X = <u><em>amount of syrup that people put on their pancakes</em></u>
The z-score probability distribution for the normal distribution is given by;
Z = ~ N(0,1)
where, = mean amount of syrup = 63 mL
= standard deviation = 13 mL
So, the distribution of X ~ N().
Let = <u><em>sample mean amount of syrup that people put on their pancakes</em></u>
The z-score probability distribution for the sample mean is given by;
Z = ~ N(0,1)
where, = mean amount of syrup = 63 mL
= standard deviation = 13 mL
n = sample of people = 43
So, the distribution of ~ N(
).
(b) If a single randomly selected individual is observed, the probability that this person consumes is between 61.4 mL and 62.8 mL is given by = P(61.4 mL < X < 62.8 mL)
P(61.4 mL < X < 62.8 mL) = P(X < 62.8 mL) - P(X 61.4 mL)
P(X < 62.8 mL) = P( <
) = P(Z < -0.02) = 1 - P(Z
0.02)
= 1 - 0.50798 = 0.49202
P(X 61.4 mL) = P(
) = P(Z
-0.12) = 1 - P(Z < 0.12)
= 1 - 0.54776 = 0.45224
Therefore, P(61.4 mL < X < 62.8 mL) = 0.49202 - 0.45224 = 0.0398.
(c) For the group of 43 pancake eaters, the probability that the average amount of syrup is between 61.4 mL and 62.8 mL is given by = P(61.4 mL < < 62.8 mL)
P(61.4 mL < < 62.8 mL) = P(
< 62.8 mL) - P(
61.4 mL)
P( < 62.8 mL) = P(
<
) = P(Z < -0.10) = 1 - P(Z
0.10)
= 1 - 0.53983 = 0.46017
P(
61.4 mL) = P(
) = P(Z
-0.81) = 1 - P(Z < 0.81)
= 1 - 0.79103 = 0.20897
Therefore, P(61.4 mL < X < 62.8 mL) = 0.46017 - 0.20897 = 0.2512.
(d) Yes, for part (d), the assumption that the distribution is normally distributed necessary.