Question

Asked Oct 10, 2019

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involving the computation of probabilities for Bernoulli trials.

(1) At least 7 successes in 10 trials with p = 0.3

(2) At least 4 failures in 8 trials with p = 0.55

Step 1

**Introduction:**

If *X* ~ Bin (*n*, *p*), then *X* represents the number of successes in *n* trials with probability of success in each trial being *p*, and the probability mass function of *X* is:

*p* (*x*) = (* _{n}*C

Step 2

**Part a:**

Here, number of trials is the sample size, *n* = 10.

The probability of success is, *p* = 0.3.

Thus, the probability of at least 7 successes in 10 trials with *p* = 0.3 is:

*P* (*X* ≥ 7)

= 1 – *P* (*X* < 7)

= 1 – *P* (*X* ≤ 6)

≈ 1 – 0.9894 [*P* (*X* ≤ 6), using Excel...

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