Question

1, Determine μx and σx from the given parameters of the population and sample size.

μ= 80​, σ= 27​, n= 81

ux =

σx =

2, A certain flight arrives on time 8080 percent of the time. Suppose 117117 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that

​(a) exactly 103 flights are on time.

​(b) at least 103 flights are on time.

​(c) fewer than 99 flights are on time.

​(d) between 99 and 107​, inclusive are on time.

​

a) ​P(103)=.                              ​(Round to four decimal places as​ needed.)

​(b) ​P(X≥103​)=                        ​(Round to four decimal places as​ needed.)

​(c) ​P(X<99)=.                         ​(Round to four decimal places as​ needed.)

​(d) ​P(99≤X≤107)=.                 ​(Round to four decimal places as​ needed.)

3,The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with a mean of 1263 chips and a standard deviation of 118 chips.

​

​(a) The 27th percentile for the number of chocolate chips in a bag of chocolate chip cookies is_____ chocolate chips.

​(Round to the nearest whole number as​ needed.)

​(b) The number of chocolate chips in a bag that make up the middle 95​% of bags is ___ to ___ chocolate chips.

​(Round to the nearest whole number as needed. Use ascending​ order.)

​(c) The interquartile range of the number of chocolate chips is___.

​(Round to the nearest whole number as​ needed.)

            

Suppose a simple random sample of size n =1000 is obtained from a population whose size is N=1,500,000 and whose population proportion with a specified characteristic is p=0.49. Complete parts​ (a) through​ (c) below.

​(a) Describe the sampling distribution of p^.

A.

Approximately​ normal, mu Subscript ModifyingAbove p with caretμpequals=0.490.49 and sigma Subscript ModifyingAbove p with caretσpalmost equals≈0.00040.0004

B.

Approximately​ normal, mu Subscript ModifyingAbove p with caretμpequals=0.490.49 and sigma Subscript ModifyingAbove p with caretσpalmost equals≈0.01580.0158

C.

Approximately​ normal, mu Subscript ModifyingAbove p with caretμpequals=0.490.49 and sigma Subscript ModifyingAbove p with caretσpalmost equals≈0.00020.0002

​(b) What is the probability of obtaining xequals=510510 or more individuals with the​ characteristic?

​P(xgreater than or equals≥510510​)equals=nothing ​(Round to four decimal places as​ needed.)

​(c) What is the probability of obtaining xequals=450450 or fewer individuals with the​ characteristic?

​P(xless than or equals≤450450​)equals=nothing ​(Round to four decimal places as​ needed.)

​

Please try to answear all part

Answer 1