Question

1.The combined SAT scores for the students at a local high school are normally distributed with a mean of 1495 and a standard deviation of 309. The local college includes a minimum score of 908 in its admission requirements.

What percentage of students from this school earn scores that satisfy the admission requirement?
P(X > 908) =  %

Enter your answer as a percent accurate to 1 decimal place (do not enter the "%" sign). Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

2.About % of the area under the curve of the standard normal distribution is outside the interval z=[−2.42,2.42]z=[-2.42,2.42] (or further than 2.42 standard deviations from the mean). Give your answer to two decimal places.

3.Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.6-in and a standard deviation of 1-in. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 3.2% or largest 3.2%.

What is the minimum head breadth that will fit the clientele?
min =

What is the maximum head breadth that will fit the clientele?
max =

Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

Refer Standard normal table/Z-table to find the probability OR use excel formula "=NORM.S.DIST(-1.8997, TRUE)" to find the probability.

Convert to percentgae

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Refer Standard normal table/Z-table to find the probability OR use excel formula "=NORM.S.DIST(2.42, TRUE)" & "=NORM.S.DIST(-2.42, TRUE)" to find the probability.

Convert to percentgae

About % of the area under the curve of the standard normal distribution is outside the interval z=[−2.42,2.42].

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Let "X" be the head breadth that will fit the clientele

Refer Standard normal table/Z-table, Lookup for z-score corresponding to area 0.032 to the left of the normal curve OR use excel formula "=NORM.S.INV(0.032)" to find the z-score.

Round to one decimal place.

Refer Standard normal table/Z-table, Lookup for z-score corresponding to area 0.032 to the right of the normal curve OR use excel formula "=NORM.S.INV(1-0.032)" to find the z-score.

Round to one decimal place.