Adult male heights have a normal probability distribution with a mean of 70 inches and a standard deviation of 4 inches. What is the probability that a randomly selected male is more than 74 inches tall? Enter you answer in decimal form, e.g. 0.68, not 68 or 68%.

Answer:The probability that the man is greater than 74 inches is 0.1587Step-by-step explanation:The required probability is found by evaluating the area under the corresponding distribution curve for the corresponding valuesThe standard normal variate factor (Z) is given by[tex]Z=\frac{x-\bar {X}}{\sigma }[/tex]where[tex]\bar{x}[/tex] is mean of the data [tex]\sigma [/tex] is the standard deviation of the data Thus corresponding to x = 74 the Z factor equals[tex]Z=\frac{74-70}{4}=1[/tex]Using the standard normal distribution table corresponding to mean of 70 and deviation of 4 the area under the curve corresponding to Z = 1 equals 0.1587