Question

(8) Let *x* be a random variable that represents the
level of glucose in the blood (milligrams per deciliter of blood)
after a 12 hour fast. Assume that for people under 50 years old,
*x* has a distribution that is approximately normal, with
mean *μ* = 54 and estimated standard deviation *σ* =
11. A test result *x* < 40 is an indication of severe
excess insulin, and medication is usually prescribed.

(a) What is the probability that, on a single test, *x*
< 40? (Round your answer to four decimal places.)

(b) Suppose a doctor uses the average x for two tests taken
about a week apart. What can we say about the probability
distribution of x? *Hint*: See Theorem 6.1.

What is the probability that x < 40? (Round your answer to four decimal places.)

(c) Repeat part (b) for *n* = 3 tests taken a week apart.
(Round your answer to four decimal places.)

(d) Repeat part (b) for *n* = 5 tests taken a week apart.
(Round your answer to four decimal places.)

Explain what this might imply if you were a doctor or a nurse.

(9) Let *x* represent the dollar amount spent on
supermarket impulse buying in a 10-minute (unplanned) shopping
interval. Based on a certain article, the mean of the *x*
distribution is about $27 and the estimated standard deviation is
about $9.

(a) Consider a random sample of *n* = 100 customers, each
of whom has 10 minutes of unplanned shopping time in a supermarket.
From the central limit theorem, what can you say about the
probability distribution of *x*, the average amount spent by
these customers due to impulse buying? What are the mean and
standard deviation of the *x* distribution?

Is it necessary to make any assumption about the *x*
distribution? Explain your answer.

(b) What is the probability that *x* is between $25 and
$29? (Round your answer to four decimal places.)

(c) Let us assume that *x* has a distribution that is
approximately normal. What is the probability that *x* is
between $25 and $29? (Round your answer to four decimal
places.)

(d) In part (b), we used *x*, the *average* amount
spent, computed for 100 customers. In part (c), we used *x*,
the amount spent by only *one* customer. The answers to
parts (b) and (c) are very different. Why would this happen?

10) A European growth mutual fund specializes in stocks from the
British Isles, continental Europe, and Scandinavia. The fund has
over 325 stocks. Let *x* be a random variable that
represents the monthly percentage return for this fund. Suppose
*x* has mean *μ* = 1.4% and standard deviation
*σ* = 1.1%.

(a) Let's consider the monthly return of the stocks in the fund
to be a sample from the population of monthly returns of all
European stocks. Is it reasonable to assume that *x* (the
average monthly return on the 325 stocks in the fund) has a
distribution that is approximately normal? Explain.

(Blank) *x* is a mean of a sample of
*n* = 325 stocks. By the(Blank) the *x*
distribution( Blank) approximately normal?

(b) After 9 months, what is the probability that the
*average* monthly percentage return x will be between 1% and
2%? (Round your answer to four decimal places.)(c)After 18 months,
what is the probability that the *average* monthly
percentage return x will be between 1% and 2%? (Round your answer
to four decimal places.

(d) Compare your answers to parts (b) and (c). Did the
probability increase as *n* (number of months) increased?
Why would this happen?

(e) If after 18 months the average monthly percentage return
*x* is more than 2%, would that tend to shake your
confidence in the statement that *μ* = 1.4%? If this
happened, do you think the European stock market might be heating
up? (Round your answer to four decimal
places.) *P*(*x* > 2%)

Explain:

Answer #1

Answer)

8)

As the given data has normal distribution, we can use standard normal z table to estimate the answers

Given mean = 54

S.d = 11

Z = (x-mean)/s.d

A)

We need to find

P(x<40)

Z = (40-54)/11

Z = -1.27

From z table, p(z<-1.27) = 0.1020

B)

In case of a sample

Z = (x-mean)/(s.d/√n)

N = 2 here

Z = (40-54)/(11/√2)

Z = -1.8

From z table, p(z<-1.8) = 0.0359

C)

N = 3

Z = (40-54)/(11/√3)

Z = -2.2

From z table, p(z<-2.2) = 0.0139

D)

N = 5

Z = (40-54)/(11/√5)

Z = -2.85

From z table, p(z<-2.85) = 0.0022

Let x be a random variable that represents the level of
glucose in the blood (milligrams per deciliter of blood) after a
12-hour fast. Assume that for people under 50 years old, x
has a distribution that is approximately normal, with mean
μ = 57 and estimated standard deviation σ = 34. A
test result x < 40 is an indication of severe excess
insulin, and medication is usually prescribed.
(a) What is the probability that, on a single test,...

Let x be a random variable that represents the level of
glucose in the blood (milligrams per deciliter of blood) after a 12
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has a distribution that is approximately normal, with mean
? = 59 and estimated standard deviation ? = 45. A
test result x < 40 is an indication of severe excess
insulin, and medication is usually prescribed.
(a) What is the probability that, on a single...

Let x be a random variable that represents the level of glucose
in the blood (milligrams per deciliter of blood) after a 12 hour
fast. Assume that for people under 50 years old, x has a
distribution that is approximately normal, with mean μ = 60 and
estimated standard deviation σ = 44. A test result x < 40 is an
indication of severe excess insulin, and medication is usually
prescribed. (a) What is the probability that, on a single...

Let x be a random variable that represents the level of glucose
in the blood (milligrams per deciliter of blood) after a 12 hour
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prescribed. (a) What is the probability that, on a single...

Let x be a random variable that represents the level of
glucose in the blood (milligrams per deciliter of blood) after a 12
hour fast. Assume that for people under 50 years old, x
has a distribution that is approximately normal, with mean
μ = 56 and estimated standard deviation σ = 42. A
test result x < 40 is an indication of severe excess
insulin, and medication is usually prescribed.
(a) What is the probability that, on a single...

Let x be a random variable that represents the level of
glucose in the blood (milligrams per deciliter of blood) after a
12-hour fast. Assume that for people under 50 years old, x
has a distribution that is approximately normal, with mean
μ = 92 and estimated standard deviation σ = 40. A
test result x < 40 is an indication of severe excess
insulin, and medication is usually prescribed.
(a) What is the probability that, on a single test,...

Let x be a random variable that represents the level of glucose
in the blood (milligrams per deciliter of blood) after a 12 hour
fast. Assume that for people under 50 years old, x has a
distribution that is approximately normal, with mean μ = 62 and
estimated standard deviation σ = 31. A test result x < 40 is an
indication of severe excess insulin, and medication is usually
prescribed.
(a) What is the probability that, on a single...

Let x be a random variable that represents the level of
glucose in the blood (milligrams per deciliter of blood) after a 12
hour fast. Assume that for people under 50 years old, x has a
distribution that is approximately normal, with mean μ = 60 and
estimated standard deviation σ = 46. A test result x < 40 is an
indication of severe excess insulin, and medication is usually
prescribed.
(a) What is the probability that, on a single...

Let x be a random variable that represents the level of
glucose in the blood (milligrams per deciliter of blood) after a 12
hour fast. Assume that for people under 50 years old, x
has a distribution that is approximately normal, with mean
μ = 90and estimated standard deviation σ = 49. A
test result x < 40 is an indication of severe excess
insulin, and medication is usually prescribed.
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Let x be a random variable that represents the level of
glucose in the blood (milligrams per deciliter of blood) after a
12-hour fast. Assume that for people under 50 years old, x
has a distribution that is approximately normal, with mean
μ = 78 and estimated standard deviation σ = 45. A
test result x < 40 is an indication of severe excess
insulin, and medication is usually prescribed.
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