Question

In Exercises 22-23, find the indicated probabilities and interpret the results. 22. Refer to Exercise 15. A random sample of 2 years is selected. Find the probability that the mean amount of black carbon emissions for the sample is (a) less than 12.3 gigagrams per year, (b) between 15.4 and 19.6 gigagrams per year, and (c) greater than 17.7 gigagrams per year Compare your answers with those in Exercise 15. 23. The mean ACT composite score in a recent year is 20.8. A random sample of 36 ACT composite scores is selected. What is the probability that the mean score for the sample is (a) less than 21.6, (b) more than 198, and (c) between 20.5 and 21.5? Assume ơ-56. (Source: ACT, Inc)

Answer 1

for problem 22 ; details given in excercise 15 is required.

23)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	20.8
std deviation   =σ=	5.6000
sample size       =n=	36
std error=σx̅=σ/√n=	0.9333

a)

probability =

P(X<21.6)

=

P(Z<0.86)=

0.8051

b)

probability =

P(X>19.8)

=

P(Z>-1.07)=

1-P(Z<-1.07)=

1-0.1423=

0.8577

c)

probability =

P(20.5<X<21.5)

=

P(-0.32<Z<0.75)=

0.7734-0.3745=

0.3989