The standard error is the ______ a variance of b variance of the sampling distribution of c standard deviation of the sampling d
1 answer:
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Answer:
x ≈ - 6.74, 0.74
Step-by-step explanation:
x² + 6x - 5 = 0 ( add 5 to both sides )
x² + 6x = 5
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(3)x + 9 = 5 + 9
(x + 3)² = 14 ( take square root of both sides )
x + 3 = ± ( subtract 3 from both sides )
x = - 3 ±
Then
x = - 3 - ≈ - 6.74 ( to the nearest hundredth )
x = - 3 + ≈ 0.74 ( to the nearest hundredth )
Answer:
(a) Probability that a single randomly selected element X of the population is between 57,000 and 58,000 = 0.46411
(b) Probability that the mean of a sample of size 100 drawn from this population is between 57,000 and 58,000 = 0.99621
Step-by-step explanation:
We are given that a normally distributed population has mean 57,800 and standard deviation 75, i.e.; = 57,800 and
= 750.
Let X = randomly selected element of the population
The z probability is given by;
Z = ~ N(0,1)
(a) So, P(57,000 <= X <= 58,000) = P(X <= 58,000) - P(X < 57,000)
P(X <= 58,000) = P( <=
) = P(Z <= 0.27) = 0.60642
P(X < 57000) = P( <
) = P(Z < -1.07) = 1 - P(Z <= 1.07)
= 1 - 0.85769 = 0.14231
Therefore, P(31 < X < 40) = 0.60642 - 0.14231 = 0.46411 .
(b) Now, we are given sample of size, n = 100
So, Mean of X, X bar = 57,800 same as before
But standard deviation of X, s = =
= 75
The z probability is given by;
Z = ~ N(0,1)
Now, probability that the mean of a sample of size 100 drawn from this population is between 57,000 and 58,000 = P(57,000 < X bar < 58,000)
P(57,000 <= X bar <= 58,000) = P(X bar <= 58,000) - P(X bar < 57,000)
P(X bar <= 58,000) = P( <=
) = P(Z <= 2.67) = 0.99621
P(X < 57000) = P( <
) = P(Z < -10.67) = P(Z > 10.67)
This probability is that much small that it is very close to 0
Therefore, P(57,000 < X bar < 58,000) = 0.99621 - 0 = 0.99621 .