Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X < 81) - P(Y < ) × (Z < d. Find the probability that more than 75 favor a charter school using the normal approximation and the table

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Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a
charter school for grades K through 5. A simple random sample of 144 is surveyed.
a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places.
O =
b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the
table. Round off to 4 decimal places.
Y - N(
c. Find the probability that at most 81 favor a charter school using the normal approximation and the table.
(Round off to z-values up to 2 decimal places.)
P(X < 81) - P(Y <
(Z <
d. Find the probability that more than 75 favor a charter school using the normal approximation and the table.
(Round off to z-values up to 2 decimal places.)
P(X > 75) - P(Y >
a (Z >
e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table.
(Round off to z-values up to 2 decimal places.)
P(X = 81) - P(
<Y< =
<Z <
||
Transcribed Image Text:Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X < 81) - P(Y < (Z < d. Find the probability that more than 75 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X > 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P( <Y< = <Z < ||
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