Question

1. Given that *x* is a normal variable with mean
*μ* = 112 and standard deviation *σ* = 14, find the
following probabilities. (Round your answers to four decimal
places.)

(a) *P*(*x* ≤ 120)

(b) *P*(*x* ≥ 80)

(c) *P*(108 ≤ *x* ≤ 117)

2. Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 8.8 minutes and a standard deviation of 1.9 minutes. For a randomly received emergency call, find the following probabilities. (Round your answers to four decimal places.)

(a) the response time is between 5 and 10 minutes

(b) the response time is less than 5 minutes

(c) the response time is more than 10 minutes

3. In the following problem, check that it is appropriate to use
the normal approximation to the binomial. Then use the normal
distribution to estimate the requested probabilities.

Do you take the free samples offered in supermarkets? About 58% of
all customers will take free samples. Furthermore, of those who
take the free samples, about 41% will buy what they have sampled.
Suppose you set up a counter in a supermarket offering free samples
of a new product. The day you were offering free samples, 301
customers passed by your counter. (Round your answers to four
decimal places.)

(a) What is the probability that more than 180 will take your
free sample?

(b) What is the probability that fewer than 200 will take your free
sample?

(c) What is the probability that a customer will take a free sample
and buy the product? Hint: Use the multiplication rule for
*dependent* events. Notice that we are given the conditional
probability *P*(buy|sample) = 0.41, while *P*(sample)
= 0.58.

(d) What is the probability that between 60 and 80 customers will
take the free sample *and* buy the product? *Hint:*
Use the probability of success calculated in part (c).

Answer #1

Given that x is a normal variable with mean μ
= 51 and standard deviation σ = 6.5, find the following
probabilities. (Round your answers to four decimal places.)
(a) P(x ≤ 60)
(b) P(x ≥ 50)
(c) P(50 ≤ x ≤ 60)

Given that x is a normal variable with mean μ
= 48 and standard deviation σ = 6.2, find the following
probabilities. (Round your answers to four decimal places.)
(a) P(x ≤ 60)
(b) P(x ≥ 50)
(c) P(50 ≤ x ≤ 60)

Given that x is a normal variable with mean μ = 111 and standard
deviation σ = 14, find the following probabilities. (Round your
answers to four decimal places.) (a) P(x ≤ 120) (b) P(x ≥ 80) (c)
P(108 ≤ x ≤ 117)

7. A normal random variable x has mean μ = 1.7
and standard deviation σ = 0.17. Find the probabilities of
these X-values. (Round your answers to four decimal
places.)
(a) 1.00 < X <
1.60
(b) X > 1.39
(c) 1.25 < X < 1.50
8. Suppose the numbers of a particular type of bacteria in
samples of 1 millilitre (mL) of drinking water tend to be
approximately normally distributed, with a mean of 81 and a
standard deviation of 8. What...

Given that x is a normal variable with mean ? = 114 and standard
deviation ? = 12, find the following probabilities. (Round your
answers to four decimal places.) (a) P(x ? 120) (b) P(x ? 80) (c)
P(108 ? x ? 117)

(1)Given that x is a normal variable with mean μ = 52 and
standard deviation σ = 6.9, find the following probabilities.
(Round your answers to four decimal places.) (a) P(x ≤ 60) (b) P(x
≥ 50) (c) P(50 ≤ x ≤ 60) (2) Find z such that 15% of the area under
the standard normal curve lies to the right of z. (Round your
answer to two decimal places.) (3) The University of Montana ski
team has six entrants...

Police response time to an emergency call is the difference
between the time the call is first received by the dispatcher and
the time a patrol car radios that it has arrived at the scene. Over
a long period of time, it has been determined that the police
response time has a normal distribution with a mean of 10.0 minutes
and a standard deviation of 1.5 minutes. For a randomly received
emergency call, find the following probabilities. (Round your
answers...

Police response time to an emergency call is the difference
between the time the call is first received by the dispatcher and
the time a patrol car radios that it has arrived at the scene. Over
a long period of time, it has been determined that the police
response time has a normal distribution with a mean of 9.2 minutes
and a standard deviation of 2.1 minutes. For a randomly received
emergency call, find the following probabilities. (Round your
answers...

Police response time to an emergency call is the difference
between the time the call is first received by the dispatcher and
the time a patrol car radios that it has arrived at the scene. Over
a long period of time, it has been determined that the police
response time has a normal distribution with a mean of 7.6 minutes
and a standard deviation of 2.3 minutes. For a randomly received
emergency call, find the following probabilities. (Round your
answers...

Police response time to an emergency call is the difference
between the time the call is first received by the dispatcher and
the time a patrol car radios that it has arrived at the scene. Over
a long period of time, it has been determined that the police
response time has a normal distribution with a mean of 8.8 minutes
and a standard deviation of 1.9 minutes. For a randomly received
emergency call, find the following probabilities. (Round your
answers...

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