Question

In: Statistics and Probability

The sugar bear candy factory makes two types of chocolate candy bars milk chocolate and milk...

The sugar bear candy factory makes two types of chocolate candy bars milk chocolate and milk chocolate with almonds. In a typical day, 40% of the candy bars are being made of milk chocolate with almonds and the rest is plain milk chocolate. At the end of the day, a quality control expert randomly chooses 14 candy bars for inspection.

a. What is the probability that fewer than 6 of the candy bars contained almonds?

b.What is the probability that at least 3 of the candy bars contained almonds?

c.What is the probability that between 5 and 9 of the candy bars contained almonds?

d.What is the probability none of the candy bars contained almonds?

e.What is the variance for the number of candy bars with almonds?

f.What is the standard deviation for the number of candy bars with almonds?

Solutions

Expert Solution

Let X denotes the number of milk chocolate with almonds among randomly chosen 14 candy bars,

Here,

X ~ Binomial(n = 14, p = 0.4)

The probability mass function of X is

a) The probability that fewer than 6 of the candy bars contained almonds

b) The probability that at least 3 of the candy bars contained almonds

c) The probability that between 5 and 9 of the candy bars contained almonds

d) The probability none of the candy bars contained almonds

e) The variance for the number of candy bars with almonds

f) The standard deviation for the number of candy bars with almonds

orchestra answered 2 years ago
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