400Hw09ans

# 400Hw09ans - STAT 400 Spring 2011 Homework #9 (due Friday,...

This preview shows pages 1–4. Sign up to view the full content.

STAT 400 Spring 2011 Homework #9 (due Friday, April 1, by 3:00 p.m.) 1. a) Suppose that the actual amount of instant coffee a filling machine puts into "6-ounce" c a n s v a r i e s f r o m c a n t o c a n a n d t h a t t h e a c t u a l f i ll may be considered a random variable h a v i n g a n o r m a l d i s t r i b u t i o n , w i t h a m e a n o f 6 . 0 3 ounces and a standard deviation of 0.04 o u n c e s . S u p p o s e a c a s e c o n t a i n s 1 2 c a n s a n d c a n b e considered as a random sample of c a n s . W h a t i s t h e p r o b a b i l i t y t h a t t h e a v e r a g e f i ll in a case is below 6 ounces? μ = 6.03, σ = 0.04, n = 12. Want P( X < 6 ) = ? S i n c e t h e d i s t r i b u t i o n w e s a m p l e f r o m i s n o r m a l , . n Z X = - σ μ P ( ) = - < 12 04 . 0 03 . 6 6 Z P = P( Z - 2.60 ) = 0.0047 . b) Suppose that the actual amount of instant coffee a filling machine puts into "6-ounce" c a n s v a r i e s f r o m c a n t o c a n a n d t h a t t h e a c t u a l f i ll may be considered a random variable h a v i n g a n o r m a l d i s t r i b u t i o n , w i t h a s t a n d a r d d e v i ation of 0.04 ounces. If on average o n l y 3 o u t o f e v e r y 2 0 0 c a n s c o n t a i n l e s s t h a n 6 o unces of coffee, what must be the m e a n f i l l o f t h e s e c a n s ? N o r m a l d i s t r i b u t i o n , μ = ? Know that P( X < 6 ) = 200 3 = 0.015. Find z such that P( Z < z ) = 0.015. T h e a r e a t o t h e l e f t i s 0 . 0 1 5 ( l e s s t h a n 0 . 5 0 ) . U s i n g t h e s t a n d a r d n o r m a l t a b l e , z = 2.17 . x = μ + σ z . 6 = μ + 0.04 (– 2.17). μ = 6.0868 oz .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2. S u p p o s e t h a t 6 0 % o f a l l v o t e r s i n a c e r t a i n c o u n t y favor a tax increase to pay for a b e t t e r s c h o o l s y s t e m . A r a n d o m s a m p l e o f 4 0 0 v o ters is selected. Use Normal a p p r o x i m a t i o n t o f i n d t h e f o l l o w i n g : B i n o m i a l ( 4 0 0 , 0 . 6 0 ) . μ = 240, σ = 9.798. a) What is the probability that more than 250 of the sample members favor the tax i n c r e a s e ? P ( X > 2 5 0 ) = P ( X > 2 5 0 . 5 ) = P ( Z > 1 . 0 7 ) = 0.1423 . b) What is the probability that at least 260 of the sample members favor the tax i n c r e a s e ? P ( X 260 ) = P( X > 259.5 ) = P( Z > 1.99 ) = 0.0233 . c) What is the probability that at most 235 of the sample members favor the tax i n c r e a s e ? P ( X 235 ) = P( X < 235.5 ) = P( Z < – 0.46 ) = 0.3228 . d) What is the probability that between 225 and 245 (both inclusive) of the sample m e m b e r s f a v o r t h e t a x i n c r e a s e ? P ( 2 2 5 X 245 ) = P( 224.5 < X < 245.5 ) = P( – 1.58 < Z < 0.56 ) = 0.6552 . e) What is the probability that exactly 234 of the sample members favor the tax i n c r e a s e ? C o m p a r e t h e a n s w e r w i t h t h e e x a c t p r o b a bility. P ( X = 2 3 4 ) = P ( 2 3 3 . 5 < X < 2 3 4 . 5 ) = P ( 0.66 < Z < – 0.56 ) = 0.0331 . B i n o m i a l : P ( X = 2 3 4 ) = () 166 234 40 . 0 60 . 0 234 400 = 0.033565 .
3. S u p p o s e t h e n u m b e r o f e - m a i l m e s s a g e s r e c e i v e d b y Mike follows Poisson d i s t r i b u t i o n w i t h t h e a v e r a g e r a g e o f 4 2 m e s s a g e s per week. Use Normal a p p r o x i m a t i o n t o f i n d t h e f o l l o w i n g : P o i s s o n , λ = 42.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## 400Hw09ans - STAT 400 Spring 2011 Homework #9 (due Friday,...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online