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

-----------------------------------------------------------------------------------------------------

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].**

-----------------------------------------------------------------------------------------------------

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.

The combined SAT scores for the students at a local high school
are normally distributed with a mean of 1471 and a standard
deviation of 294. The local college includes a minimum score of
1706 in its admission requirements.
What percentage of students from this school earn scores that
satisfy the admission requirement?
P(X > 1706) = %
Enter your answer as a percent accurate to 1 decimal place (do not
enter the "%" sign). Answers obtained using exact z-scores
or...

The combined SAT scores for the students at a local high school
are normally distributed with a mean of 1528 and a standard
deviation of 309. The local college includes a minimum score of 848
in its admission requirements.
What percentage of students from this school earn scores that fail
to satisfy the admission requirement?
P(X < 848) = %
Enter your answer as a percent accurate to 1 decimal place (do not
enter the "%" sign). Answers obtained using exact...

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 5.8-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 0.9% or largest 0.9%.
What is the minimum head breadth that will fit the clientele?
min =...

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 6.2-in and a standard deviation
of 1.1-in. Due to financial constraints, the helmets will be
designed to fit all men except those with head breadths that are in
the smallest 3.5% or largest 3.5%. What is the minimum head breadth
that will fit the clientele? min =...

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 2.1% or largest 2.1%. What is the minimum head breadth
that will fit the clientele? min =...

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 6.4-in and a standard deviation
of 0.9-in. Due to financial constraints, the helmets will be
designed to fit all men except those with head breadths that are in
the smallest 1.1% or largest 1.1%. What is the minimum head breadth
that will fit the clientele? min =...

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 6.8-in and a standard deviation
of 0.8-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% or largest 3%.
What is the minimum head breadth that will fit the clientele?
min =...

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 6.2-in and a standard deviation
of 1.1-in. Due to financial constraints, the helmets will be
designed to fit all men except those with head breadths that are in
the smallest 2.6% or largest 2.6%. What is the minimum head breadth
that will fit the clientele? min =...

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 7.1-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 4.5% or largest 4.5%. What is the minimum head breadth
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min =...

Multiple question needing guidance please.
1. A distribution of values is normal with a mean of 173.2 and a
standard deviation of 39.
Find the probability that a randomly selected value is between
200.5 and 298.
P(200.5 < X < 298) =_______________
2. A distribution of values is normal with a mean of 229.7 and a
standard deviation of 83.5.
Find P32, which is the score separating the
bottom 32% from the top 68%.
P32 = __________________
3. Engineers must...

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