Question

Charles, Julia, and Alex are in grades 4, 3, and 2, respectively, and are representing their school at a spelling bee. The school's team score is the sum of the number of words the individual students spell correctly out of 100 words each. Different words are given for each grade level. From practicing at school, it is known that the probability of spelling each word correctly is 0.91 for Charles and 0.83 for the younger two, Julia and Alex.

(a) Find the mean, μ, and standard deviation, σ, for the number of correct words for each child. (Round all answers for σ to three decimal places.)

for Charles

μ	=
σ	=

for Julia

μ	=
σ	=

for Alex

μ	=
σ	=

(b) Find the mean, μ, and standard deviation, σ, for the team score. (Round the answer for σ to the nearest hundredth.)

(c) Assume that the individual scores are independent. Does the team score have a binomial distribution

Explain why.
Because the probability of correctly spelling a word is  ---Select--- the same not the same  for all three children.

(d) The team score would be approximately normal with the mean and standard deviation you were asked to find in part (b). If last year's team score was 264, what is the approximate probability, P that this year's team scores as well or better? (Round the answer to four decimal places.)

Answer 1

a) or Charles

mean E(x)=μ=np=91

standard deviation σ=√(np(1-p))=2.862

for Julia

mean E(x)=μ=np=83

standard deviation σ=√(np(1-p))=3.756

for Alex

mean E(x)=μ=np=83

standard deviation σ=√(np(1-p))=3.756

b)

μ =91+83+83 =257

σ=sqrt(Var(x1)+Var(x2)+Var(x3)) =6.03

c)No

Because the probability of correctly spelling a word is not the same  for all three children.

d)

probability =P(X>264)=P(Z>(264-257)/6.03)=P(Z>1.16)=1-P(Z<1.16)=1-0.877=0.1230