Its already in a fraction
Answer and Step-by-step explanation: P(X) calculated by the binomial probability formula is:
P(X) = .
P(20) =
P(20) =
P(20) = 0.0552
To determine whether the normal distribution can be used to estimate this probability, both n.p and n.(1-p) must be greater than 5:
n . p = 53*0.3 = 15.9
n.(1-p) = 53(1-0.3) = 37.1
Since both ARE greater than 5, normal distribution can be used.
To approximate:
mean = n . p = 15.9
standard deviation = = 3.34
Find the z-score:
z = =
z-score = 0.8907
Comparing values:
0.8907 - 0.0552 = 0.8355
The answer i got was 120666.6 dollars
I hope this helps you :)
A) 180 would be expected to pass.
B) The standard deviation is 4.
C) 95% of people would fall between 172 and 188.
D) Yes, this is more than 3 standard deviations below the mean.
Explanation
A) Multiply the probability by the sample size:
0.6(300) = 180
B) Standard deviation is found by:
√n(p)(1-p)
For our data, we have:
√300(0.6)(0.4) = 4
C) Two standard deviations below the mean is 180-2(4) = 172; two standard deviations above the mean is 180+2(4)= 188.
D) Three standard deviations below the mean is 180-3(4) = 168; 134 is more than this below the mean. 99.7% of data fall within 3 standard deviations of the mean; 0.15% fall below this point, so yes, this is unusually low.