Answer:
he made an error, the probability that his homeruns traveled at least 380 feet is 65.54%
Step-by-step explanation:
let´s see the Robinson's calculation:
using the formula for normal distribution:
Z = (x-μ)(σ/[tex]\sqrt{n}[/tex]) [1]
where:
x is raw measurement
μ is the mean
σ is the standar deviation
n is the size of sample
in this case x = 380, μ = 394, σ = 35, n = 1.
then using the equation [1] he calculated the Z score:
[tex]Z = \frac{380-394}{\frac{35}{\sqrt{1}}}\\\\Z = -\frac{14}{35}\\\\Z = -0.4\\\\[/tex]
and it's correct but his answer is wrong because he confuse the term at least.
at least means that the probability be greater than 380 feet, not less than 380 feet.
so he looked the Z score in a table of normal distribution (this table has been attached) and effectively this value is 0.3446. but as I told you this probability is for x < 380.
therefore, the probability that his homeruns traveled at least 380 feet is:
[tex]P(x > 380) = 1 - P(x < 380)\\\\P(x > 380) = 1 - 0.3446\\\\P(x > 380) = 0.6554 \ or \ 65.54 \%[/tex]
please see the table attached.
