Question

If , what is the smallest value of that satisfies the requirements for a normally distributed ?.

Answer 1

Using Normal distribution and sample proportion, the smallest possible value of n is 25 for which the distribution is normal .

Sample proportion:

Sample proportions are obtained in the following situations:

• if the population proportions of the variables under investigation are normally distributed.
• if the random sample is from this population.
• if the sample size is large enough to include at least 5 of the 2 possible outcomes.

we have given that

The value of probability (p) = 3/5 = 0.6 It is necessary that for the value of n probability of normal distribution satisfied the required condition,

• np≥ 10
• n(1- p ) ≥10

if both of above conditions are satisfied then the distribution is Normal .

we have to find smallest value of n such that the distribution become normal .

Now, n× 0.6 ≥ 10

=> n ≥ 16.6

and n (1 - p) ≥ 10

=> n(1 - 0.6) ≥ 10

=> n × 0.4 ≥ 10

=> n ≥ 25

Hence, the smallest value of n is 25

To learn more about sample proportion, refer:

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Complete question:

If p = 3/5, what is the smallest value of n that satisfies the requirements for a normally distributed p?