Question

In: Statistics and Probability

Recent research indicated that about 20 % of children in a certain country are deficient in...

Recent research indicated that about 20 % of children in a certain country are deficient in vitamin D. A company that sells vitamin D supplements tests 370 elementary school children in one area of the country. Use a Normal approximation to find the probability that no more than 59 of them have vitamin D deficiency.

Solutions

Expert Solution

Solution:

Given that,

P = 0.20

1 - P = 0.80

n = 370

Here, BIN ( n , P ) that is , BIN (370 , 0.20)

then,

n*p = 370*0.20 = 74 > 5

n(1- P) = 370*0.80 = 296 > 5

According to normal approximation binomial,

X Normal

Mean = = n*P = 74

Standard deviation = =n*p*(1-p) = 370*0.20*0.80= 59.2

We using countinuity correction factor

P( X a ) = P(X < a + 0.5)

P(x < 59.5) = P((x - ) / < (59.5 - 74) / 59.2)

= P(z < -1.88)

= 0.0301

The probability that no more than 59 of them have vitamin D deficiency is  0.0301


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