(19.28) To estimate the mean score μ of those who took the Medical College Admission Test on your campus, you will obtain the scores of an SRS of students. From published information you know that the scores are approximately Normal with standard deviation about 6.6. You want your sample mean x¯¯¯ to estimate μ with an error of no more than 1.4 point in either direction.

What standard deviation (±0.0001) must x¯ have so that 99.7% of all samples give an x¯ within 1.4 point of μ?

standard deviation = ±0.4667

Step-by-step explanation:

In Normal distribution, approximately 68% of all the data lie within 1 standard deviation from the mean, approximately 95% of all the data lie within 2 standard deviations from the mean and approximately 99.7% of all the data lie within 3 standard deviations from the mean.

Therefore, for a confidence interval of 99.7% the standard deviation of the x¯ must be 3 standard deviations from the mean,

3σ = ±1.4

σ = ±1.4/3

σ = ±0.4667

Therefore, 0.4667 is the standard deviation that x¯ must have so that 99.7% of all samples give an x¯ within 1.4 point of μ.

answer: b.

step-by-step explanation:

the y coordinate for point b is 0, and answer b is the only one with that y coordinate.

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752