Question

A new muscle relaxant is available. Researchers from the firm
developing the relaxant have done studies that indicate that the
time lapse between administration of the drug and beginning effects
of the drug is normally distributed, with mean *μ* = 38
minutes and standard deviation *σ* = 5 minutes.

(a) The drug is administered to one patient selected at random.
What is the probability that the time it takes to go into effect is
35 minutes or less? (Round your answer to four decimal
places.)

(b) The drug is administered to a random sample of 10 patients.
What is the probability that the average time before it is
effective for all 10 patients is 35 minutes or less? (Round your
answer to four decimal places.)

(c) Comment on the differences of the results in parts (a) and
(b).

The probability in part (b) is ---Select--- smaller
than larger than the same as part (a) because
the ---Select--- mean standard deviation
is ---Select--- larger smaller for the *x*
distribution.

Answer #1

a)

for normal distribution z score =(X-μ)/σx | |

here mean= μ= | 38 |

std deviation =σ= | 5.0000 |

probability = | P(X<35) | = | P(Z<-0.6)= | 0.2743 |

b)

sample size =n= | 10 |

std error=σ_{x̅}=σ/√n= |
1.5811 |

probability = | P(X<35) | = | P(Z<-1.9)= | 0.0287 |

c)

The probability in part (b) is smaller than as part (a) because the standard deviation is smaller for the x distribution.

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done studies that indicate that the time lapse between
administration of the drug and beginning effect of the drug is
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(A) The drug is administered to
one patient selected at random. What is the probability that the
time it takes to go into effect is 35 minutes or less?
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