please show work needed to find final answer...thumbs up if typed/ or written ne

Question

please show work needed to find final answer...thumbs up if typed/ or written neatly.

473 Dentists' use of laughing gas. According to the American 0% of all dentists use nitrous oxide 4173 Dentis Dental Association, 6 in their practice. If x equals the number of dentists in a random sample of five dentists who use laughing gas in practice, then the probability distribution of x is 2 4 p(x) .0102 .0768 2304 3456 2592 0778 a. Verify that the probabilities for x sum to 1. b. Find P(x = 4) c. Find P(xr

Explanation / Answer

a) Total = 1

Yes add up to 1

b) P(x=4) = 0.2592

c) P(X<2) = 0.0102+0.0768

= 0.0870

d) P(X>=3) = 0.3456+0.2592+0.0778

= 0.6826

e) E(x) = mean of x

= sum of x p(x)

= 0+0.0768+0.4608+1.0368+1.0368+0.3890

= 3.0002

This is the value of average which is expected

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