Naomi has earned $63 mowing lawns the past two days. She worked 1 hours yesterday and 3 hours
1 answer:
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Answer:
The probability that an elementary or secondary school teacher selected at random from this city is a female or holds a second job is 0.90.
Step-by-step explanation:
Denote the events as follows:
<em>X</em> = an elementary or secondary school teacher from a city is a female
<em>Y</em> = an elementary or secondary school teacher holds a second job
The information provided is:
P (X) = 0.66
P (Y) = 0.46
P (X ∩ Y) = 0.22
The addition rule of probability is:
Use this formula to compute the probability that an elementary or secondary school teacher selected at random from this city is a female or holds a second job as follows:
Thus, the probability that an elementary or secondary school teacher selected at random from this city is a female or holds a second job is 0.90.
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.