PLEASE HELP Two transmitters are prepared to send signals from a control tower to a receiver at a station a few miles away. To save on costs, the transmitters are not used equally.
Transmitter A is used 10% of the time and transmitter B is used 90% of the time. The receiver module is 75% effective at decoding the signal for transmitter A but only 30% effective for decoding the signal for transmitter B. The intelligence agency needs to be assured that the signals will be received and decoded at least 40% of the time so it doesn’t need to waste energy and money resending. Will this happen in this scenario?

tip $2.90

total $17.40

wth is with the little mtn top and what are you talking about like fix your words and accually make sence with them and i like was in a completly different question like three times like it seems like your ilitteret

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.