An electronics firm claims that the proportion of defective units of a certain process is 5%. A buyer has a standard procedure of inspecting 15 units selected randomly from a large lot. On a particular occasion, the bury found 5 items defective. a) What is the probability of this occurrence, given that the claim of 5% defective is correct

0.0006 = 0.06% probability of this occurrence

Step-by-step explanation:

For each unit, there are only two possible outcomes. Either it is defective, or it is not. The probability of an unit being defective is independent of any other unit, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

An electronics firm claims that the proportion of defective units of a certain process is 5%.

This means that

A buyer has a standard procedure of inspecting 15 units selected randomly from a large lot.

This means that

a) What is the probability of this occurrence?

Probability of 5 defective items, whch is P(X = 5). So

0.0006 = 0.06% probability of this occurrence

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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