A new drug is found to be 70% effective in curing a certain kind of skin illness. From a pool of patients who had received the drug after being diagnosed with the illness, 12 of them are randomly selected. Assume a considerable amount of time has passed between a patient being administered the drug and the selection then occuring (to ensure the drug's effectiveness or lackthereof in treating a patient). Answer the following:   a) What is the likelihood that exactly 5 of the twelve patients chosen have been cured of the illness? b) a) What is the likelihood that at most 5 of the twelve patients chosen have been cured of

A survey showed that 81% of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. If 20 adults are randomly selected, find the probability that no more than 1 of them need correction for their eyesight. Is 1 a significantly low number of adults requiring eyesight correction? The probability that no more than 1 of the 20 adults require eyesight correction is (Round to three decimal places as needed.)

Physicians at a clinic gave what they thought were drugs to 890890 asthma, ulcer, and herpes patients. Although the doctors later learned that the drugs were really placebos, 5555 % of the patients reported an improved condition. Assume that if the placebo is ineffective, the probability of a patients condition improving is 0.530.53. For the hypotheses that the proportion of improving is 0.530.53 against that it is >0.53>0.53, find the p-value. ?=p=

In a genetics experiment on​ peas, one sample of offspring contained 396 green peas and 296 yellow peas. Based on those​ results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of 34 that was​ expected?

In a genetics experiment on peas, one sample of offspring contained 367 green peas and 40 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the valuee of 3/4 that was expected?

A survey showed that 79​% of adults need correction​ (eyeglasses, contacts,​ surgery, etc.) for their eyesight. If 15 adults are randomly​ selected, find the probability that at least 14 of them need correction for their eyesight. Is 14 a significantly high number of adults requiring eyesight​ correction? The probability that at least 14 of the 15 adults require eyesight correction is nothing. ​(Round to three decimal places as​ needed.)