Transcriptional bursting is a fundamental property of genes in which transcription from DNA to mRNA can occur in "bursts" or "pulses". Consider the experiment of observing the number of mRNA transcriptions until observing four "bursts." Suppose the probability of a burst in gene expression is 6.5%. Suppose another researcher is only interested in the number of mRNA until the first "burst". What is the probability that 18 mRNA transcripts are made until the 1st burst?

A certain insecticide kills 60% of all insects in laboratory experiments. A sample of 12 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 6 insects will die? Round your answer to four decimal places.

Suppose that you toss a coin n times and experimentally determine that the probability of heads is 40%. How many times must you toss the coin in order to be 95% certain that the theoretical probability for heads is between 38% and 42%?

The useful life of Johnson rods for use in a particular vehicle follows an exponential distribution with an average useful life of 5.2 years.You have a three-year warranty on your vehicle’s Johnson rod. What is the probability that the Johnson rod doesn’t fail before then? That is, what is the probability that its useful life doesn’t end before three years?b.If the vehicle manufacturer wants to limit the number of claims on the three-year warranty to 20%, what should the average useful life of the Johnson rod be?

Suppose the average tread-life of a certain brand of tire is 45,000 miles and that this mileage follows the exponential probability distribution. What is the probability that a randomly selected tire will have a tread-life between 30,000 and 50,000 miles?

A certain insecticide kills 70% of all insects in laboratory experiments. A sample of 11 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 22 insects will die? Round your answer to four decimal places.

A certain insecticide kills 70% of all insects in laboratory experiments. A sample of 14 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 10 insects will die? Round your answer to four decimal places.

A certain insecticide kills 60%60% of all insects in laboratory experiments. A sample of 99 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 55 insects will survive? Round your answer to four decimal places.

A certain insecticide kills 60% of all insects in laboratory experiments. A sample of 7 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 3 insects will die? Round your answer to four decimal places.