g A psychic was tested for extrasensory perception (ESP). The psychic was presented with cards face down and asked to determine if each of the cards was one of four symbols: a star, cross, circle, or square. Let p represent the probability that the psychic correctly identified the symbols on the cards in a random trial. How large a sample n would you need to estimate p with margin of error 0.01 and 95% confidence?

The sample size should be 6157

Step-by-step explanation:

Given that the margin of error (e) = ± 0.01 and the confidence (C) = 95% = 0.95.

Let us assume that the guess p = 0.25 as the value of p.

α = 1 - C = 1 - 0.95 = 0.05

The Z score of α/2 is the same as the z score of 0.475 (0.5 - 0.025) which is 1.96. Therefore

To determine the sample size n, we use the formula:

let y equal to

the total fare and x is the mile of taxi ride. so the equation is

y = 0.55x + 1.75

since susie has

$10 to spend for a taxi cab, so he can have

10 = 0.55x +

1.75

x = 15 miles of

taxi ride

so the system of

inequality is

10 < 0.55x +

1.75

x > 2

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: