Question

A population of values has a nornal distribution with μ sample of size n = 41. 214 and σ 22.5. You intend to draw a random Find the probability that a single randomly selected value is between 208.4 and 223.1. P(208.4<X< 223.1)- Find the probability that a sample of size n 41 is randomly selected with a mean between 208.4 and 223.1. P(208.4< M< 223.1)- Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted Points possible: 1 License Unlimited attempts. Submit

Answer 1

1)a)

for normal distribution z score =(X-μ)/σx
a)
b)here mean=       μ=	214
std deviation   =σ=	22.5000
probability =	P(208.4<X<223.1)	=	P(-0.25<Z<0.4)=	0.6571-0.4017=	0.2553
b) sample size   =n=	41
std error=σx̅=σ/√n=	3.5139

probability =

P(208.4<X<223.1)

=

P(-1.59<Z<2.59)=

0.9952-0.0555=

0.9397

2)

for normal distribution z score =(p̂-p)/σp
here population proportion=     p=	0.750
sample size       =n=	177
std error of proportion=σp=√(p*(1-p)/n)=	0.0325

probability =

P(0.66<X<0.84)

=

P(-2.77<Z<2.77)=

0.9972-0.0028=

0.9944