Find the area under the standard normal curve to the right of z = 2.12.

Answer to #1

P(z > 2.12) = 0.50  0.483 = 0.017

Answer to #2

P(z<1.93) = 0.50 + 0.4732 = 0.9732

Answer to #3

P(z<-1.33) = 0.50  0.4082 = 0.0918

Answer to #4

By inspecting the function P(x) we see it satisfies the following binomial properties: n = 4, p = 0.5, q = 0.5 (p + q = 1), the two exponents x and 4-x add up to n = 4, and x can take on any integer value from zero to n = 4; therefore P(x) is a binomial probability function.

Answer to #5

x is a binomial random variable because the trials are independent. n = 4, the number of trials; two outcomes, success = ace and failure = not ace; p = P(ace) = 4/52 and q = P(not ace) = 48/52; x = n (aces drawn in 4 trials) and could be any number 0, 1, 2, 3 or 4 . Further, the probability of success (get an ace) remains 4/52 for each trial throughout the experiment, as long as the card drawn on each trial is replaced before the next trial occurs.

Answer to #6

x is not a binomial random variable because the trials are not independent. The
probability of success (get an ace) changes from trial to trial. On the first trial it is 4/52.
The probability of an ace on the second trial depends on the outcome of the first trial; it is
4/51 if an ace is not selected, and it is 3/51 if an ace was selected. The probability of an
ace on any given trial continues to change when the experiment is completed without
replacement.

Answer to #7

x is a binomial variable since it satisfies the following properties:
n = 75 repeated identical independent trials (towels), there are only two outcome (first
quality, irregular), p =P(success) = P(irregular), x = number of irregular towels that may
take on any integer value from 0 to 75.

Answer to #8

The distribution of the sample is somewhat similar to that of the given distribution. The two highest probabilities in the random data occurred at x = 1 and 3, matching the two highest probabilities for the given distribution. Also, the two lowest probabilities in the random data occurred at x = 4 and 5, matching the two lowest probabilities for the given distribution. Finally, the probability in the random data occurred at x = 2 is identical to that for the given distribution.

Answer to #9

All possible outcomes are accounted for.