question archive Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu equals 131 days μ=131 days and standard deviation sigma equals 8 days σ=8 days
Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu equals 131 days μ=131 days and standard deviation sigma equals 8 days σ=8 days
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Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu equals 131 days
μ=131 days and standard deviation sigma equals 8 days
σ=8 days. Complete parts? (a) through? (f) below.
?(a) What is the probability that a randomly selected pregnancy lasts less than 128
128 ?days?
The probability that a randomly selected pregnancy lasts less than 128
128 days is approximately
0.352
0.352. ?(Round to four decimal places as? needed.)
Interpret this probability. Select the correct choice below and fill in the answer box within your choice.
?(Round to the nearest integer as? needed.)
A.
If 100 pregnant individuals were selected independently from this? population, we would expect
35
35 pregnancies to last less than 128
128 days.
Your answer is correct.
B.
If 100 pregnant individuals were selected independently from this? population, we would expect
nothing
pregnancies to last more than 128
128 days.
C.
If 100 pregnant individuals were selected independently from this? population, we would expect
nothing
pregnancies to last exactly 128
128 days.
?(b) Suppose a random sample of 19
19 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.
The sampling distribution of x overbar
x is normal
with mu Subscript x overbar
μxequals
=
131
131 and sigma Subscript x overbar
σxequals
=
nothing
.
?(Round to four decimal places as? needed.)
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a) ?=0.352?
A. If 100 pregnant individuals were selected independently from this? population, we would expect 35 pregnancies to last less than 128 days.
b) The sampling distribution of the sample mean will be normal with mean ?μx??=μ=131? and ?σx??? ?=1.8353?
Step-by-step explanation
a) The probability that a randomly selected pregnancy lasts less than 128
We need to find ?P(X<128)?
?=P(z<σ128−μ?)?
?=P(z<8128−131?)?
?=P(z<−0.38)?
?=0.352?
A. If 100 pregnant individuals were selected independently from this? population, we would expect 35 pregnancies to last less than 128 days.
?(b) Suppose a random sample of 19 pregnancies is obtained. Describe the sampling distribution
The sampling distribution of the sample mean will be normal with mean ?μx??=μ=131? and ?σx??? ?=n?σ?=19?8?=1.8353?
