Monday

December 22, 2014

December 22, 2014

Posted by **Writeacher** on Wednesday, June 6, 2007 at 1:45pm.

What is the probability, in a random poll of 60 children from the ages of 0 to 11 that more than 15 children are in day care at least 20h per week?

p(k)= nCk P^k (1-p)^n-k

were

n= 60

p=0.32

k= 15

q= 1-0.32= 0.68

so:

p(k) = 60C15 x 0.32^15 (0.68) ^60-15

= 0.0583464079

is this correct?

What is the probability in a random poll of 60 children that fewer than 20 are in a day care at least 20h per week?

How would I do this because it says fewer?

Answer is incorrect.

You could answer this exactly by using a combinatorial application as you have tried to do, or you could approximate the answer using the properties of a binominal distribution. I will use the latter. (The formula you gave is the would give the probability of observing EXACTLY 15 children.)

With 60 kids we would expect .32*60=19.2 kids to be in day care. This estimate has an estimated standard deviation of sqrt(n*p*q) = sqrt(60*.32*.68) = 3.613. Now then you want to know the likelyhood of observing more than 15 kids. (I will use a mid-point of 15.5) So, 19.2-15.5 = 3.7. This is (3.7/3.613)=1.02 standard deviations below the mean. Looking in my Cumulative Normal Distribution table, 1.02 corresponds to .8461. ERGO, there is approximately an 85% chance of observing more than 15 children out of a sample of 60 will be in day care.

Follow the same steps for estimating the number fewer than 20. It should be slightly greater than 50%.

**Answer this Question**

**Related Questions**

economyst check! - In many families both parents work, as a result there is ...

English - I really need help with my writing. I need some to proof read a paper...

geometry - Need help with a word problem - Carrie collected can food for a ...

Working with Parents - Why must parents be involved in their child's day care ...

cultural diversity-reposted question - Which scenario best describes a nuclear ...

Algebra - Of two-car families in a small city, 88% remain two-car families in ...

English Grammar - Mother's Day is the second Sunday in May in America. Americans...

math - 1.Thompson Security has been hired to determine the number of visitors at...

math - Omega System Services, a member of the Omega Health Foundation operates a...

Roles of Women - How does this relate to life for women colonists in the ...