A fair six-sided number cube is rolled 60 times. What is the probability that fewer than 10% of the rolls are a five? Find the z-table here.

0.0823 = 8.23% probability that fewer than 10% of the rolls are a five

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation .

A fair six-sided number cube is rolled 60 times.

This means that

Rolls that are a five:

For each roll, there are 6 possible outcomes: 1, 2, 3, 4, 5 or 6. So the probability of rolling a five is:

The distribution has mean and standard deviation:

What is the probability that fewer than 10% of the rolls are a five?

This is the pvalue of Z when X = 0.1. So

By the Central Limit Theorem

has a pvalue of 0.0823

0.0823 = 8.23% probability that fewer than 10% of the rolls are a five

answer: what do you mean

answer: a. 13/44

step-by-step explanation: judging by the information given to us, we are looking for experimental probability. we can see that 13 males have chosen chocolate ice cream. there are 44 ice creams in total (remember that the total is always the denominator). so our answer is 13/44.