Assume that men's weights are normally distributed with a mean of 172 lb and a standard deviation of 29 lb. if 4 man is randomly selected, find the probability that they have a mean weight between 160 lb and 180 lb.(up to four decimal place, )

 0.5056

Step-by-step explanation:

Let x be the random variable that represents the readings on scientific thermometers .

Given : The men's weights are normally distributed,

Population mean :

Standard deviation :

Sample size : n=4

Z-score :

Now, the z-value corresponding to 160  :  

z-value corresponding to 180  :  

By using standard normal distribution table for z-values,

P-value =

Hence, the probability that they have a mean weight between 160 lb and 180 lb = 0.5056

Hence, the probability of the reading greater than -1.05 in degrees Celsius.= 0.8531

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