According to a research institution, men spent an average of exist134.13 on Vale

Question

According to a research institution, men spent an average of exist134.13 on Valentine's Day gifts in 2009. Assume the standard deviation for this population is exist35 and that it is normally distributed. A random sample of 10 men who celebrate Valentine's Day was selected. Complete parts a through e. a. Calculate the standard error of the mean. sigma_x^- = b. What is the probability that the sample mean will be less than exist125? P(x exist145) = d. What is the probability that the sample mean will be between exist120 and exist165? P(exist120 lessthanorequalto x lessthanorequalto exist165) =

Explanation / Answer

mean = 134.13 , s = 35 , n = 10

a) Standard error = s / sqrt(n)
= 35 / sqrt(10)
= 11.07

b)
P(x < 125)

z = ( x - mean) / ( s/sqrt(n))
= ( 125 - 134.13) / 11.07
= -0.825
P(X < 125) = P( z < -0.825) = 0.2048

c)

P(x > 145)

z = ( x - mean) / ( s/sqrt(n))
= ( 145 - 134.13) / 11.07
= 0.982
P(X > 145) = P( z < 0.982) = 0.1631

d)

P(120 < x < 165)

z = ( x - mean) / ( s/sqrt(n))
= ( 120 - 134.13) / 11.07
= -1.276

z = ( x - mean) / ( s/sqrt(n))
= ( 165 - 134.13) / 11.07
= 2.788
P(120 < X < 165) = P(-1.276 < z < 2.788) = 0.8965

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