Question

1. A person's level of blood glucose and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 73 and standard deviation of σ = 20. What is the probability that, for an adult after a 12-hour fast, x is more than 85? a. 0.113 b. 0.363 c. 0.226 d. 0.726 e. 0.274 2. . Suppose that x has a distribution with μ = 14 and σ = 8. If a random sample is taken of size n = 53, find . a. 8.00 b. 1.10 c. 1.92 d. 30.29 e. 14.00 Can someone explain how to do these in a way I could understand? Thank you so much in advance!

Answer 1

1_)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	73
std deviation   =σ=	20.000

probability =P(X>85)=P(Z>(85-73)/20)=P(Z>0.6)=1-P(Z<0.6)=1-0.7257=0.274

option E is correct

(Note:

if using ti-84 use command :normalcdf(85,1000000,73,20)

if using excel use command :1-norm.dist(85,73,20,true)

2)(here after find, symbol is not shown, if it is  σ_x̅ answer is 1.1

std deviation   =σ=	8.000
sample size       =n=	53

std error=σx̅=σ/√n=8/sqrt(53)=

1.10