1. A statistics professor plans classes so carefully that the lengths of her cla

Question

1. A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 47.0 and 52.0 minutes. Find the probability that a given class period runs between 51.5 and 51.75 minutes.

Find the probability of selecting a class that runs between 51.5 and 51.75 minutes.

_____(Round to three decimal places as needed.)

2. Assume that women's heights are normally distributed with a mean given by =62.5 in, and a standard deviation given by =2.8 in.

(a) If 1 woman is randomly selected, find the probability that her height is less than 63 in.

(b) If 46 women are randomly selected, find the probability that they have a mean height less than 63 in.

Explanation / Answer

1) for paramter of uniform distribution a=47 and b=52

therefore probability of selecting a class that runs between 51.5 and 51.75 minutes=P(51.5<X<51.75)

=(51.75-51.5)/(52-47)=0.05

2) a)probability that her height is less than 63 in =P(X<63) =P(Z<(63-62.5)/2.8)=P(Z<0.1786)=0.5709

b)

for n=46 ; std error =std deviation/(n)1/2 =2.8/(46)1/2 =0.4128

probability that mean height is less than 63 in =P(X<63) =P(Z<(63-62.5)/0.4128)=P(Z<1.2111)=0.8871

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