What is $2.63 in cents? A 2.63¢ 263¢ C 0.263¢
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Answer:
P(X<45)= 0.0401
Step-by-step explanation:
Hello!
The study variable is:
X: Hardness of heat-treated parts.
This variable has a normal distribution with μ= 48.5 and standard deviation δ= 2
You need to calculate the probability of the parts being below the minimum specified hardness. If the lowest specificated hardness of heat-treated parts is 45, then:
P(X<45)
To calculate this probability you have to use the standard normal distribution: Z=(X-μ)/δ~N(0;1)
Using the information of the mean and standard deviation of the population you have to standardize the value of X so that you can use the tabulated Z-distribution to reach the asked probability:
P(Z<(45-48.5)/2)= P(Z<-1.75)
Since the value is negative you have to look for the probability in the left Z-table. The integer and first decimal, -1.7* value is in the first column and the second integer is in the first row, *.*5. When you cross them you find the corresponding probability.
P(Z<-1.75)= 0.0401
(sketch of distribution and table are attached)
I hope it helps!
